Highly Composite Numbers (Anti-Primes)

Thursday, December 6, 2018
By: Matthew Doucette

Highly composite numbers have more factors than any number smaller than themselves. In other words, they are numbers with a high degree of factorization or divisibility. This is the opposite of a prime number, which has no factors (other than 1 and itself).

Highly Composite Numbers (HCMs) and Factorizations:

1: 1.

2: 1, 2.

4: 1, 2, 4.

6: 1, 2, 3, 6.

12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.

180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.

240: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.

360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360.

720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720.

840: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840.

1260: 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260.

1680: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680.

2520: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520.

5040: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 105, 112, 120, 126, 140, 144, 168, 180, 210, 240, 252, 280, 315, 336, 360, 420, 504, 560, 630, 720, 840, 1008, 1260, 1680, 2520, 5040.

7560: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 54, 56, 60, 63, 70, 72, 84, 90, 105, 108, 120, 126, 135, 140, 168, 180, 189, 210, 216, 252, 270, 280, 315, 360, 378, 420, 504, 540, 630, 756, 840, 945, 1080, 1260, 1512, 1890, 2520, 3780, 7560.

10080: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 210, 224, 240, 252, 280, 288, 315, 336, 360, 420, 480, 504, 560, 630, 672, 720, 840, 1008, 1120, 1260, 1440, 1680, 2016, 2520, 3360, 5040, 10080.

15120: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 336, 360, 378, 420, 432, 504, 540, 560, 630, 720, 756, 840, 945, 1008, 1080, 1260, 1512, 1680, 1890, 2160, 2520, 3024, 3780, 5040, 7560, 15120.

20160: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 280, 288, 315, 320, 336, 360, 420, 448, 480, 504, 560, 576, 630, 672, 720, 840, 960, 1008, 1120, 1260, 1344, 1440, 1680, 2016, 2240, 2520, 2880, 3360, 4032, 5040, 6720, 10080, 20160.

25200: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 100, 105, 112, 120, 126, 140, 144, 150, 168, 175, 180, 200, 210, 225, 240, 252, 280, 300, 315, 336, 350, 360, 400, 420, 450, 504, 525, 560, 600, 630, 700, 720, 840, 900, 1008, 1050, 1200, 1260, 1400, 1575, 1680, 1800, 2100, 2520, 2800, 3150, 3600, 4200, 5040, 6300, 8400, 12600, 25200.

27720: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 110, 120, 126, 132, 140, 154, 165, 168, 180, 198, 210, 220, 231, 252, 264, 280, 308, 315, 330, 360, 385, 396, 420, 440, 462, 495, 504, 616, 630, 660, 693, 770, 792, 840, 924, 990, 1155, 1260, 1320, 1386, 1540, 1848, 1980, 2310, 2520, 2772, 3080, 3465, 3960, 4620, 5544, 6930, 9240, 13860, 27720.

45360: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 81, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 162, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 324, 336, 360, 378, 405, 420, 432, 504, 540, 560, 567, 630, 648, 720, 756, 810, 840, 945, 1008, 1080, 1134, 1260, 1296, 1512, 1620, 1680, 1890, 2160, 2268, 2520, 2835, 3024, 3240, 3780, 4536, 5040, 5670, 6480, 7560, 9072, 11340, 15120, 22680, 45360.

50400: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 56, 60, 63, 70, 72, 75, 80, 84, 90, 96, 100, 105, 112, 120, 126, 140, 144, 150, 160, 168, 175, 180, 200, 210, 224, 225, 240, 252, 280, 288, 300, 315, 336, 350, 360, 400, 420, 450, 480, 504, 525, 560, 600, 630, 672, 700, 720, 800, 840, 900, 1008, 1050, 1120, 1200, 1260, 1400, 1440, 1575, 1680, 1800, 2016, 2100, 2400, 2520, 2800, 3150, 3360, 3600, 4200, 5040, 5600, 6300, 7200, 8400, 10080, 12600, 16800, 25200, 50400.

55440: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 165, 168, 176, 180, 198, 210, 220, 231, 240, 252, 264, 280, 308, 315, 330, 336, 360, 385, 396, 420, 440, 462, 495, 504, 528, 560, 616, 630, 660, 693, 720, 770, 792, 840, 880, 924, 990, 1008, 1155, 1232, 1260, 1320, 1386, 1540, 1584, 1680, 1848, 1980, 2310, 2520, 2640, 2772, 3080, 3465, 3696, 3960, 4620, 5040, 5544, 6160, 6930, 7920, 9240, 11088, 13860, 18480, 27720, 55440.

83160: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 40, 42, 44, 45, 54, 55, 56, 60, 63, 66, 70, 72, 77, 84, 88, 90, 99, 105, 108, 110, 120, 126, 132, 135, 140, 154, 165, 168, 180, 189, 198, 210, 216, 220, 231, 252, 264, 270, 280, 297, 308, 315, 330, 360, 378, 385, 396, 420, 440, 462, 495, 504, 540, 594, 616, 630, 660, 693, 756, 770, 792, 840, 924, 945, 990, 1080, 1155, 1188, 1260, 1320, 1386, 1485, 1512, 1540, 1848, 1890, 1980, 2079, 2310, 2376, 2520, 2772, 2970, 3080, 3465, 3780, 3960, 4158, 4620, 5544, 5940, 6930, 7560, 8316, 9240, 10395, 11880, 13860, 16632, 20790, 27720, 41580, 83160.

110880: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 160, 165, 168, 176, 180, 198, 210, 220, 224, 231, 240, 252, 264, 280, 288, 308, 315, 330, 336, 352, 360, 385, 396, 420, 440, 462, 480, 495, 504, 528, 560, 616, 630, 660, 672, 693, 720, 770, 792, 840, 880, 924, 990, 1008, 1056, 1120, 1155, 1232, 1260, 1320, 1386, 1440, 1540, 1584, 1680, 1760, 1848, 1980, 2016, 2310, 2464, 2520, 2640, 2772, 3080, 3168, 3360, 3465, 3696, 3960, 4620, 5040, 5280, 5544, 6160, 6930, 7392, 7920, 9240, 10080, 11088, 12320, 13860, 15840, 18480, 22176, 27720, 36960, 55440, 110880.

166320: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 99, 105, 108, 110, 112, 120, 126, 132, 135, 140, 144, 154, 165, 168, 176, 180, 189, 198, 210, 216, 220, 231, 240, 252, 264, 270, 280, 297, 308, 315, 330, 336, 360, 378, 385, 396, 420, 432, 440, 462, 495, 504, 528, 540, 560, 594, 616, 630, 660, 693, 720, 756, 770, 792, 840, 880, 924, 945, 990, 1008, 1080, 1155, 1188, 1232, 1260, 1320, 1386, 1485, 1512, 1540, 1584, 1680, 1848, 1890, 1980, 2079, 2160, 2310, 2376, 2520, 2640, 2772, 2970, 3024, 3080, 3465, 3696, 3780, 3960, 4158, 4620, 4752, 5040, 5544, 5940, 6160, 6930, 7560, 7920, 8316, 9240, 10395, 11088, 11880, 13860, 15120, 16632, 18480, 20790, 23760, 27720, 33264, 41580, 55440, 83160, 166320.

221760: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 55, 56, 60, 63, 64, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 105, 110, 112, 120, 126, 132, 140, 144, 154, 160, 165, 168, 176, 180, 192, 198, 210, 220, 224, 231, 240, 252, 264, 280, 288, 308, 315, 320, 330, 336, 352, 360, 385, 396, 420, 440, 448, 462, 480, 495, 504, 528, 560, 576, 616, 630, 660, 672, 693, 704, 720, 770, 792, 840, 880, 924, 960, 990, 1008, 1056, 1120, 1155, 1232, 1260, 1320, 1344, 1386, 1440, 1540, 1584, 1680, 1760, 1848, 1980, 2016, 2112, 2240, 2310, 2464, 2520, 2640, 2772, 2880, 3080, 3168, 3360, 3465, 3520, 3696, 3960, 4032, 4620, 4928, 5040, 5280, 5544, 6160, 6336, 6720, 6930, 7392, 7920, 9240, 10080, 10560, 11088, 12320, 13860, 14784, 15840, 18480, 20160, 22176, 24640, 27720, 31680, 36960, 44352, 55440, 73920, 110880, 221760.

277200: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 50, 55, 56, 60, 63, 66, 70, 72, 75, 77, 80, 84, 88, 90, 99, 100, 105, 110, 112, 120, 126, 132, 140, 144, 150, 154, 165, 168, 175, 176, 180, 198, 200, 210, 220, 225, 231, 240, 252, 264, 275, 280, 300, 308, 315, 330, 336, 350, 360, 385, 396, 400, 420, 440, 450, 462, 495, 504, 525, 528, 550, 560, 600, 616, 630, 660, 693, 700, 720, 770, 792, 825, 840, 880, 900, 924, 990, 1008, 1050, 1100, 1155, 1200, 1232, 1260, 1320, 1386, 1400, 1540, 1575, 1584, 1650, 1680, 1800, 1848, 1925, 1980, 2100, 2200, 2310, 2475, 2520, 2640, 2772, 2800, 3080, 3150, 3300, 3465, 3600, 3696, 3850, 3960, 4200, 4400, 4620, 4950, 5040, 5544, 5775, 6160, 6300, 6600, 6930, 7700, 7920, 8400, 9240, 9900, 11088, 11550, 12600, 13200, 13860, 15400, 17325, 18480, 19800, 23100, 25200, 27720, 30800, 34650, 39600, 46200, 55440, 69300, 92400, 138600, 277200.

332640: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 105, 108, 110, 112, 120, 126, 132, 135, 140, 144, 154, 160, 165, 168, 176, 180, 189, 198, 210, 216, 220, 224, 231, 240, 252, 264, 270, 280, 288, 297, 308, 315, 330, 336, 352, 360, 378, 385, 396, 420, 432, 440, 462, 480, 495, 504, 528, 540, 560, 594, 616, 630, 660, 672, 693, 720, 756, 770, 792, 840, 864, 880, 924, 945, 990, 1008, 1056, 1080, 1120, 1155, 1188, 1232, 1260, 1320, 1386, 1440, 1485, 1512, 1540, 1584, 1680, 1760, 1848, 1890, 1980, 2016, 2079, 2160, 2310, 2376, 2464, 2520, 2640, 2772, 2970, 3024, 3080, 3168, 3360, 3465, 3696, 3780, 3960, 4158, 4320, 4620, 4752, 5040, 5280, 5544, 5940, 6048, 6160, 6930, 7392, 7560, 7920, 8316, 9240, 9504, 10080, 10395, 11088, 11880, 12320, 13860, 15120, 15840, 16632, 18480, 20790, 22176, 23760, 27720, 30240, 33264, 36960, 41580, 47520, 55440, 66528, 83160, 110880, 166320, 332640.

498960: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 66, 70, 72, 77, 80, 81, 84, 88, 90, 99, 105, 108, 110, 112, 120, 126, 132, 135, 140, 144, 154, 162, 165, 168, 176, 180, 189, 198, 210, 216, 220, 231, 240, 252, 264, 270, 280, 297, 308, 315, 324, 330, 336, 360, 378, 385, 396, 405, 420, 432, 440, 462, 495, 504, 528, 540, 560, 567, 594, 616, 630, 648, 660, 693, 720, 756, 770, 792, 810, 840, 880, 891, 924, 945, 990, 1008, 1080, 1134, 1155, 1188, 1232, 1260, 1296, 1320, 1386, 1485, 1512, 1540, 1584, 1620, 1680, 1782, 1848, 1890, 1980, 2079, 2160, 2268, 2310, 2376, 2520, 2640, 2772, 2835, 2970, 3024, 3080, 3240, 3465, 3564, 3696, 3780, 3960, 4158, 4455, 4536, 4620, 4752, 5040, 5544, 5670, 5940, 6160, 6237, 6480, 6930, 7128, 7560, 7920, 8316, 8910, 9072, 9240, 10395, 11088, 11340, 11880, 12474, 13860, 14256, 15120, 16632, 17820, 18480, 20790, 22680, 23760, 24948, 27720, 31185, 33264, 35640, 41580, 45360, 49896, 55440, 62370, 71280, 83160, 99792, 124740, 166320, 249480, 498960.

554400: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 50, 55, 56, 60, 63, 66, 70, 72, 75, 77, 80, 84, 88, 90, 96, 99, 100, 105, 110, 112, 120, 126, 132, 140, 144, 150, 154, 160, 165, 168, 175, 176, 180, 198, 200, 210, 220, 224, 225, 231, 240, 252, 264, 275, 280, 288, 300, 308, 315, 330, 336, 350, 352, 360, 385, 396, 400, 420, 440, 450, 462, 480, 495, 504, 525, 528, 550, 560, 600, 616, 630, 660, 672, 693, 700, 720, 770, 792, 800, 825, 840, 880, 900, 924, 990, 1008, 1050, 1056, 1100, 1120, 1155, 1200, 1232, 1260, 1320, 1386, 1400, 1440, 1540, 1575, 1584, 1650, 1680, 1760, 1800, 1848, 1925, 1980, 2016, 2100, 2200, 2310, 2400, 2464, 2475, 2520, 2640, 2772, 2800, 3080, 3150, 3168, 3300, 3360, 3465, 3600, 3696, 3850, 3960, 4200, 4400, 4620, 4950, 5040, 5280, 5544, 5600, 5775, 6160, 6300, 6600, 6930, 7200, 7392, 7700, 7920, 8400, 8800, 9240, 9900, 10080, 11088, 11550, 12320, 12600, 13200, 13860, 15400, 15840, 16800, 17325, 18480, 19800, 22176, 23100, 25200, 26400, 27720, 30800, 34650, 36960, 39600, 46200, 50400, 55440, 61600, 69300, 79200, 92400, 110880, 138600, 184800, 277200, 554400.

665280: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 54, 55, 56, 60, 63, 64, 66, 70, 72, 77, 80, 84, 88, 90, 96, 99, 105, 108, 110, 112, 120, 126, 132, 135, 140, 144, 154, 160, 165, 168, 176, 180, 189, 192, 198, 210, 216, 220, 224, 231, 240, 252, 264, 270, 280, 288, 297, 308, 315, 320, 330, 336, 352, 360, 378, 385, 396, 420, 432, 440, 448, 462, 480, 495, 504, 528, 540, 560, 576, 594, 616, 630, 660, 672, 693, 704, 720, 756, 770, 792, 840, 864, 880, 924, 945, 960, 990, 1008, 1056, 1080, 1120, 1155, 1188, 1232, 1260, 1320, 1344, 1386, 1440, 1485, 1512, 1540, 1584, 1680, 1728, 1760, 1848, 1890, 1980, 2016, 2079, 2112, 2160, 2240, 2310, 2376, 2464, 2520, 2640, 2772, 2880, 2970, 3024, 3080, 3168, 3360, 3465, 3520, 3696, 3780, 3960, 4032, 4158, 4320, 4620, 4752, 4928, 5040, 5280, 5544, 5940, 6048, 6160, 6336, 6720, 6930, 7392, 7560, 7920, 8316, 8640, 9240, 9504, 10080, 10395, 10560, 11088, 11880, 12096, 12320, 13860, 14784, 15120, 15840, 16632, 18480, 19008, 20160, 20790, 22176, 23760, 24640, 27720, 30240, 31680, 33264, 36960, 41580, 44352, 47520, 55440, 60480, 66528, 73920, 83160, 95040, 110880, 133056, 166320, 221760, 332640, 665280.

720720: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 80, 84, 88, 90, 91, 99, 104, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 154, 156, 165, 168, 176, 180, 182, 195, 198, 208, 210, 220, 231, 234, 240, 252, 260, 264, 273, 280, 286, 308, 312, 315, 330, 336, 360, 364, 385, 390, 396, 420, 429, 440, 455, 462, 468, 495, 504, 520, 528, 546, 560, 572, 585, 616, 624, 630, 660, 693, 715, 720, 728, 770, 780, 792, 819, 840, 858, 880, 910, 924, 936, 990, 1001, 1008, 1040, 1092, 1144, 1155, 1170, 1232, 1260, 1287, 1320, 1365, 1386, 1430, 1456, 1540, 1560, 1584, 1638, 1680, 1716, 1820, 1848, 1872, 1980, 2002, 2145, 2184, 2288, 2310, 2340, 2520, 2574, 2640, 2730, 2772, 2860, 3003, 3080, 3120, 3276, 3432, 3465, 3640, 3696, 3960, 4004, 4095, 4290, 4368, 4620, 4680, 5005, 5040, 5148, 5460, 5544, 5720, 6006, 6160, 6435, 6552, 6864, 6930, 7280, 7920, 8008, 8190, 8580, 9009, 9240, 9360, 10010, 10296, 10920, 11088, 11440, 12012, 12870, 13104, 13860, 15015, 16016, 16380, 17160, 18018, 18480, 20020, 20592, 21840, 24024, 25740, 27720, 30030, 32760, 34320, 36036, 40040, 45045, 48048, 51480, 55440, 60060, 65520, 72072, 80080, 90090, 102960, 120120, 144144, 180180, 240240, 360360, 720720.

1081080: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 84, 88, 90, 91, 99, 104, 105, 108, 110, 117, 120, 126, 130, 132, 135, 140, 143, 154, 156, 165, 168, 180, 182, 189, 195, 198, 210, 216, 220, 231, 234, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 330, 351, 360, 364, 378, 385, 390, 396, 420, 429, 440, 455, 462, 468, 495, 504, 520, 540, 546, 572, 585, 594, 616, 630, 660, 693, 702, 715, 728, 756, 770, 780, 792, 819, 840, 858, 910, 924, 936, 945, 990, 1001, 1080, 1092, 1144, 1155, 1170, 1188, 1260, 1287, 1320, 1365, 1386, 1404, 1430, 1485, 1512, 1540, 1560, 1638, 1716, 1755, 1820, 1848, 1890, 1980, 2002, 2079, 2145, 2184, 2310, 2340, 2376, 2457, 2520, 2574, 2730, 2772, 2808, 2860, 2970, 3003, 3080, 3276, 3432, 3465, 3510, 3640, 3780, 3861, 3960, 4004, 4095, 4158, 4290, 4620, 4680, 4914, 5005, 5148, 5460, 5544, 5720, 5940, 6006, 6435, 6552, 6930, 7020, 7560, 7722, 8008, 8190, 8316, 8580, 9009, 9240, 9828, 10010, 10296, 10395, 10920, 11880, 12012, 12285, 12870, 13860, 14040, 15015, 15444, 16380, 16632, 17160, 18018, 19305, 19656, 20020, 20790, 24024, 24570, 25740, 27027, 27720, 30030, 30888, 32760, 36036, 38610, 40040, 41580, 45045, 49140, 51480, 54054, 60060, 72072, 77220, 83160, 90090, 98280, 108108, 120120, 135135, 154440, 180180, 216216, 270270, 360360, 540540, 1081080.

1441440: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 80, 84, 88, 90, 91, 96, 99, 104, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 154, 156, 160, 165, 168, 176, 180, 182, 195, 198, 208, 210, 220, 224, 231, 234, 240, 252, 260, 264, 273, 280, 286, 288, 308, 312, 315, 330, 336, 352, 360, 364, 385, 390, 396, 416, 420, 429, 440, 455, 462, 468, 480, 495, 504, 520, 528, 546, 560, 572, 585, 616, 624, 630, 660, 672, 693, 715, 720, 728, 770, 780, 792, 819, 840, 858, 880, 910, 924, 936, 990, 1001, 1008, 1040, 1056, 1092, 1120, 1144, 1155, 1170, 1232, 1248, 1260, 1287, 1320, 1365, 1386, 1430, 1440, 1456, 1540, 1560, 1584, 1638, 1680, 1716, 1760, 1820, 1848, 1872, 1980, 2002, 2016, 2080, 2145, 2184, 2288, 2310, 2340, 2464, 2520, 2574, 2640, 2730, 2772, 2860, 2912, 3003, 3080, 3120, 3168, 3276, 3360, 3432, 3465, 3640, 3696, 3744, 3960, 4004, 4095, 4290, 4368, 4576, 4620, 4680, 5005, 5040, 5148, 5280, 5460, 5544, 5720, 6006, 6160, 6240, 6435, 6552, 6864, 6930, 7280, 7392, 7920, 8008, 8190, 8580, 8736, 9009, 9240, 9360, 10010, 10080, 10296, 10920, 11088, 11440, 12012, 12320, 12870, 13104, 13728, 13860, 14560, 15015, 15840, 16016, 16380, 17160, 18018, 18480, 18720, 20020, 20592, 21840, 22176, 22880, 24024, 25740, 26208, 27720, 30030, 32032, 32760, 34320, 36036, 36960, 40040, 41184, 43680, 45045, 48048, 51480, 55440, 60060, 65520, 68640, 72072, 80080, 90090, 96096, 102960, 110880, 120120, 131040, 144144, 160160, 180180, 205920, 240240, 288288, 360360, 480480, 720720, 1441440.

2162160: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 80, 84, 88, 90, 91, 99, 104, 105, 108, 110, 112, 117, 120, 126, 130, 132, 135, 140, 143, 144, 154, 156, 165, 168, 176, 180, 182, 189, 195, 198, 208, 210, 216, 220, 231, 234, 240, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 330, 336, 351, 360, 364, 378, 385, 390, 396, 420, 429, 432, 440, 455, 462, 468, 495, 504, 520, 528, 540, 546, 560, 572, 585, 594, 616, 624, 630, 660, 693, 702, 715, 720, 728, 756, 770, 780, 792, 819, 840, 858, 880, 910, 924, 936, 945, 990, 1001, 1008, 1040, 1080, 1092, 1144, 1155, 1170, 1188, 1232, 1260, 1287, 1320, 1365, 1386, 1404, 1430, 1456, 1485, 1512, 1540, 1560, 1584, 1638, 1680, 1716, 1755, 1820, 1848, 1872, 1890, 1980, 2002, 2079, 2145, 2160, 2184, 2288, 2310, 2340, 2376, 2457, 2520, 2574, 2640, 2730, 2772, 2808, 2860, 2970, 3003, 3024, 3080, 3120, 3276, 3432, 3465, 3510, 3640, 3696, 3780, 3861, 3960, 4004, 4095, 4158, 4290, 4368, 4620, 4680, 4752, 4914, 5005, 5040, 5148, 5460, 5544, 5616, 5720, 5940, 6006, 6160, 6435, 6552, 6864, 6930, 7020, 7280, 7560, 7722, 7920, 8008, 8190, 8316, 8580, 9009, 9240, 9360, 9828, 10010, 10296, 10395, 10920, 11088, 11440, 11880, 12012, 12285, 12870, 13104, 13860, 14040, 15015, 15120, 15444, 16016, 16380, 16632, 17160, 18018, 18480, 19305, 19656, 20020, 20592, 20790, 21840, 23760, 24024, 24570, 25740, 27027, 27720, 28080, 30030, 30888, 32760, 33264, 34320, 36036, 38610, 39312, 40040, 41580, 45045, 48048, 49140, 51480, 54054, 55440, 60060, 61776, 65520, 72072, 77220, 80080, 83160, 90090, 98280, 102960, 108108, 120120, 135135, 144144, 154440, 166320, 180180, 196560, 216216, 240240, 270270, 308880, 360360, 432432, 540540, 720720, 1081080, 2162160.

2882880: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 55, 56, 60, 63, 64, 65, 66, 70, 72, 77, 78, 80, 84, 88, 90, 91, 96, 99, 104, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 154, 156, 160, 165, 168, 176, 180, 182, 192, 195, 198, 208, 210, 220, 224, 231, 234, 240, 252, 260, 264, 273, 280, 286, 288, 308, 312, 315, 320, 330, 336, 352, 360, 364, 385, 390, 396, 416, 420, 429, 440, 448, 455, 462, 468, 480, 495, 504, 520, 528, 546, 560, 572, 576, 585, 616, 624, 630, 660, 672, 693, 704, 715, 720, 728, 770, 780, 792, 819, 832, 840, 858, 880, 910, 924, 936, 960, 990, 1001, 1008, 1040, 1056, 1092, 1120, 1144, 1155, 1170, 1232, 1248, 1260, 1287, 1320, 1344, 1365, 1386, 1430, 1440, 1456, 1540, 1560, 1584, 1638, 1680, 1716, 1760, 1820, 1848, 1872, 1980, 2002, 2016, 2080, 2112, 2145, 2184, 2240, 2288, 2310, 2340, 2464, 2496, 2520, 2574, 2640, 2730, 2772, 2860, 2880, 2912, 3003, 3080, 3120, 3168, 3276, 3360, 3432, 3465, 3520, 3640, 3696, 3744, 3960, 4004, 4032, 4095, 4160, 4290, 4368, 4576, 4620, 4680, 4928, 5005, 5040, 5148, 5280, 5460, 5544, 5720, 5824, 6006, 6160, 6240, 6336, 6435, 6552, 6720, 6864, 6930, 7280, 7392, 7488, 7920, 8008, 8190, 8580, 8736, 9009, 9152, 9240, 9360, 10010, 10080, 10296, 10560, 10920, 11088, 11440, 12012, 12320, 12480, 12870, 13104, 13728, 13860, 14560, 14784, 15015, 15840, 16016, 16380, 17160, 17472, 18018, 18480, 18720, 20020, 20160, 20592, 21840, 22176, 22880, 24024, 24640, 25740, 26208, 27456, 27720, 29120, 30030, 31680, 32032, 32760, 34320, 36036, 36960, 37440, 40040, 41184, 43680, 44352, 45045, 45760, 48048, 51480, 52416, 55440, 60060, 64064, 65520, 68640, 72072, 73920, 80080, 82368, 87360, 90090, 96096, 102960, 110880, 120120, 131040, 137280, 144144, 160160, 180180, 192192, 205920, 221760, 240240, 262080, 288288, 320320, 360360, 411840, 480480, 576576, 720720, 960960, 1441440, 2882880.

3603600: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 52, 55, 56, 60, 63, 65, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 99, 100, 104, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 150, 154, 156, 165, 168, 175, 176, 180, 182, 195, 198, 200, 208, 210, 220, 225, 231, 234, 240, 252, 260, 264, 273, 275, 280, 286, 300, 308, 312, 315, 325, 330, 336, 350, 360, 364, 385, 390, 396, 400, 420, 429, 440, 450, 455, 462, 468, 495, 504, 520, 525, 528, 546, 550, 560, 572, 585, 600, 616, 624, 630, 650, 660, 693, 700, 715, 720, 728, 770, 780, 792, 819, 825, 840, 858, 880, 900, 910, 924, 936, 975, 990, 1001, 1008, 1040, 1050, 1092, 1100, 1144, 1155, 1170, 1200, 1232, 1260, 1287, 1300, 1320, 1365, 1386, 1400, 1430, 1456, 1540, 1560, 1575, 1584, 1638, 1650, 1680, 1716, 1800, 1820, 1848, 1872, 1925, 1950, 1980, 2002, 2100, 2145, 2184, 2200, 2275, 2288, 2310, 2340, 2475, 2520, 2574, 2600, 2640, 2730, 2772, 2800, 2860, 2925, 3003, 3080, 3120, 3150, 3276, 3300, 3432, 3465, 3575, 3600, 3640, 3696, 3850, 3900, 3960, 4004, 4095, 4200, 4290, 4368, 4400, 4550, 4620, 4680, 4950, 5005, 5040, 5148, 5200, 5460, 5544, 5720, 5775, 5850, 6006, 6160, 6300, 6435, 6552, 6600, 6825, 6864, 6930, 7150, 7280, 7700, 7800, 7920, 8008, 8190, 8400, 8580, 9009, 9100, 9240, 9360, 9900, 10010, 10296, 10725, 10920, 11088, 11440, 11550, 11700, 12012, 12600, 12870, 13104, 13200, 13650, 13860, 14300, 15015, 15400, 15600, 16016, 16380, 17160, 17325, 18018, 18200, 18480, 19800, 20020, 20475, 20592, 21450, 21840, 23100, 23400, 24024, 25025, 25200, 25740, 27300, 27720, 28600, 30030, 30800, 32175, 32760, 34320, 34650, 36036, 36400, 39600, 40040, 40950, 42900, 45045, 46200, 46800, 48048, 50050, 51480, 54600, 55440, 57200, 60060, 64350, 65520, 69300, 72072, 75075, 80080, 81900, 85800, 90090, 92400, 100100, 102960, 109200, 120120, 128700, 138600, 144144, 150150, 163800, 171600, 180180, 200200, 225225, 240240, 257400, 277200, 300300, 327600, 360360, 400400, 450450, 514800, 600600, 720720, 900900, 1201200, 1801800, 3603600.

4324320: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 80, 84, 88, 90, 91, 96, 99, 104, 105, 108, 110, 112, 117, 120, 126, 130, 132, 135, 140, 143, 144, 154, 156, 160, 165, 168, 176, 180, 182, 189, 195, 198, 208, 210, 216, 220, 224, 231, 234, 240, 252, 260, 264, 270, 273, 280, 286, 288, 297, 308, 312, 315, 330, 336, 351, 352, 360, 364, 378, 385, 390, 396, 416, 420, 429, 432, 440, 455, 462, 468, 480, 495, 504, 520, 528, 540, 546, 560, 572, 585, 594, 616, 624, 630, 660, 672, 693, 702, 715, 720, 728, 756, 770, 780, 792, 819, 840, 858, 864, 880, 910, 924, 936, 945, 990, 1001, 1008, 1040, 1056, 1080, 1092, 1120, 1144, 1155, 1170, 1188, 1232, 1248, 1260, 1287, 1320, 1365, 1386, 1404, 1430, 1440, 1456, 1485, 1512, 1540, 1560, 1584, 1638, 1680, 1716, 1755, 1760, 1820, 1848, 1872, 1890, 1980, 2002, 2016, 2079, 2080, 2145, 2160, 2184, 2288, 2310, 2340, 2376, 2457, 2464, 2520, 2574, 2640, 2730, 2772, 2808, 2860, 2912, 2970, 3003, 3024, 3080, 3120, 3168, 3276, 3360, 3432, 3465, 3510, 3640, 3696, 3744, 3780, 3861, 3960, 4004, 4095, 4158, 4290, 4320, 4368, 4576, 4620, 4680, 4752, 4914, 5005, 5040, 5148, 5280, 5460, 5544, 5616, 5720, 5940, 6006, 6048, 6160, 6240, 6435, 6552, 6864, 6930, 7020, 7280, 7392, 7560, 7722, 7920, 8008, 8190, 8316, 8580, 8736, 9009, 9240, 9360, 9504, 9828, 10010, 10080, 10296, 10395, 10920, 11088, 11232, 11440, 11880, 12012, 12285, 12320, 12870, 13104, 13728, 13860, 14040, 14560, 15015, 15120, 15444, 15840, 16016, 16380, 16632, 17160, 18018, 18480, 18720, 19305, 19656, 20020, 20592, 20790, 21840, 22176, 22880, 23760, 24024, 24570, 25740, 26208, 27027, 27720, 28080, 30030, 30240, 30888, 32032, 32760, 33264, 34320, 36036, 36960, 38610, 39312, 40040, 41184, 41580, 43680, 45045, 47520, 48048, 49140, 51480, 54054, 55440, 56160, 60060, 61776, 65520, 66528, 68640, 72072, 77220, 78624, 80080, 83160, 90090, 96096, 98280, 102960, 108108, 110880, 120120, 123552, 131040, 135135, 144144, 154440, 160160, 166320, 180180, 196560, 205920, 216216, 240240, 270270, 288288, 308880, 332640, 360360, 393120, 432432, 480480, 540540, 617760, 720720, 864864, 1081080, 1441440, 2162160, 4324320.

6486480: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 33, 35, 36, 39, 40, 42, 44, 45, 48, 52, 54, 55, 56, 60, 63, 65, 66, 70, 72, 77, 78, 80, 81, 84, 88, 90, 91, 99, 104, 105, 108, 110, 112, 117, 120, 126, 130, 132, 135, 140, 143, 144, 154, 156, 162, 165, 168, 176, 180, 182, 189, 195, 198, 208, 210, 216, 220, 231, 234, 240, 252, 260, 264, 270, 273, 280, 286, 297, 308, 312, 315, 324, 330, 336, 351, 360, 364, 378, 385, 390, 396, 405, 420, 429, 432, 440, 455, 462, 468, 495, 504, 520, 528, 540, 546, 560, 567, 572, 585, 594, 616, 624, 630, 648, 660, 693, 702, 715, 720, 728, 756, 770, 780, 792, 810, 819, 840, 858, 880, 891, 910, 924, 936, 945, 990, 1001, 1008, 1040, 1053, 1080, 1092, 1134, 1144, 1155, 1170, 1188, 1232, 1260, 1287, 1296, 1320, 1365, 1386, 1404, 1430, 1456, 1485, 1512, 1540, 1560, 1584, 1620, 1638, 1680, 1716, 1755, 1782, 1820, 1848, 1872, 1890, 1980, 2002, 2079, 2106, 2145, 2160, 2184, 2268, 2288, 2310, 2340, 2376, 2457, 2520, 2574, 2640, 2730, 2772, 2808, 2835, 2860, 2970, 3003, 3024, 3080, 3120, 3240, 3276, 3432, 3465, 3510, 3564, 3640, 3696, 3780, 3861, 3960, 4004, 4095, 4158, 4212, 4290, 4368, 4455, 4536, 4620, 4680, 4752, 4914, 5005, 5040, 5148, 5265, 5460, 5544, 5616, 5670, 5720, 5940, 6006, 6160, 6237, 6435, 6480, 6552, 6864, 6930, 7020, 7128, 7280, 7371, 7560, 7722, 7920, 8008, 8190, 8316, 8424, 8580, 8910, 9009, 9072, 9240, 9360, 9828, 10010, 10296, 10395, 10530, 10920, 11088, 11340, 11440, 11583, 11880, 12012, 12285, 12474, 12870, 13104, 13860, 14040, 14256, 14742, 15015, 15120, 15444, 16016, 16380, 16632, 16848, 17160, 17820, 18018, 18480, 19305, 19656, 20020, 20592, 20790, 21060, 21840, 22680, 23166, 23760, 24024, 24570, 24948, 25740, 27027, 27720, 28080, 29484, 30030, 30888, 31185, 32760, 33264, 34320, 35640, 36036, 36855, 38610, 39312, 40040, 41580, 42120, 45045, 45360, 46332, 48048, 49140, 49896, 51480, 54054, 55440, 57915, 58968, 60060, 61776, 62370, 65520, 71280, 72072, 73710, 77220, 80080, 81081, 83160, 84240, 90090, 92664, 98280, 99792, 102960, 108108, 115830, 117936, 120120, 124740, 135135, 144144, 147420, 154440, 162162, 166320, 180180, 185328, 196560, 216216, 231660, 240240, 249480, 270270, 294840, 308880, 324324, 360360, 405405, 432432, 463320, 498960, 540540, 589680, 648648, 720720, 810810, 926640, 1081080, 1297296, 1621620, 2162160, 3243240, 6486480.

7207200: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 50, 52, 55, 56, 60, 63, 65, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 96, 99, 100, 104, 105, 110, 112, 117, 120, 126, 130, 132, 140, 143, 144, 150, 154, 156, 160, 165, 168, 175, 176, 180, 182, 195, 198, 200, 208, 210, 220, 224, 225, 231, 234, 240, 252, 260, 264, 273, 275, 280, 286, 288, 300, 308, 312, 315, 325, 330, 336, 350, 352, 360, 364, 385, 390, 396, 400, 416, 420, 429, 440, 450, 455, 462, 468, 480, 495, 504, 520, 525, 528, 546, 550, 560, 572, 585, 600, 616, 624, 630, 650, 660, 672, 693, 700, 715, 720, 728, 770, 780, 792, 800, 819, 825, 840, 858, 880, 900, 910, 924, 936, 975, 990, 1001, 1008, 1040, 1050, 1056, 1092, 1100, 1120, 1144, 1155, 1170, 1200, 1232, 1248, 1260, 1287, 1300, 1320, 1365, 1386, 1400, 1430, 1440, 1456, 1540, 1560, 1575, 1584, 1638, 1650, 1680, 1716, 1760, 1800, 1820, 1848, 1872, 1925, 1950, 1980, 2002, 2016, 2080, 2100, 2145, 2184, 2200, 2275, 2288, 2310, 2340, 2400, 2464, 2475, 2520, 2574, 2600, 2640, 2730, 2772, 2800, 2860, 2912, 2925, 3003, 3080, 3120, 3150, 3168, 3276, 3300, 3360, 3432, 3465, 3575, 3600, 3640, 3696, 3744, 3850, 3900, 3960, 4004, 4095, 4200, 4290, 4368, 4400, 4550, 4576, 4620, 4680, 4950, 5005, 5040, 5148, 5200, 5280, 5460, 5544, 5600, 5720, 5775, 5850, 6006, 6160, 6240, 6300, 6435, 6552, 6600, 6825, 6864, 6930, 7150, 7200, 7280, 7392, 7700, 7800, 7920, 8008, 8190, 8400, 8580, 8736, 8800, 9009, 9100, 9240, 9360, 9900, 10010, 10080, 10296, 10400, 10725, 10920, 11088, 11440, 11550, 11700, 12012, 12320, 12600, 12870, 13104, 13200, 13650, 13728, 13860, 14300, 14560, 15015, 15400, 15600, 15840, 16016, 16380, 16800, 17160, 17325, 18018, 18200, 18480, 18720, 19800, 20020, 20475, 20592, 21450, 21840, 22176, 22880, 23100, 23400, 24024, 25025, 25200, 25740, 26208, 26400, 27300, 27720, 28600, 30030, 30800, 31200, 32032, 32175, 32760, 34320, 34650, 36036, 36400, 36960, 39600, 40040, 40950, 41184, 42900, 43680, 45045, 46200, 46800, 48048, 50050, 50400, 51480, 54600, 55440, 57200, 60060, 61600, 64350, 65520, 68640, 69300, 72072, 72800, 75075, 79200, 80080, 81900, 85800, 90090, 92400, 93600, 96096, 100100, 102960, 109200, 110880, 114400, 120120, 128700, 131040, 138600, 144144, 150150, 160160, 163800, 171600, 180180, 184800, 200200, 205920, 218400, 225225, 240240, 257400, 277200, 288288, 300300, 327600, 343200, 360360, 400400, 450450, 480480, 514800, 554400, 600600, 655200, 720720, 800800, 900900, 1029600, 1201200, 1441440, 1801800, 2402400, 3603600, 7207200.

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1081080, 1093950, 1101600, 1113840, 1130976, 1158300, 1166880, 1178100, 1179360, 1193400, 1201200, 1211760, 1225224, 1237600, 1247400, 1253070, 1276275, 1285200, 1297296, 1312740, 1336608, 1346400, 1351350, 1361360, 1378377, 1392300, 1413720, 1432080, 1441440, 1458600, 1474200, 1514700, 1531530, 1542240, 1544400, 1570800, 1575288, 1591200, 1621620, 1633632, 1640925, 1663200, 1670760, 1696464, 1701700, 1750320, 1767150, 1790100, 1801800, 1837836, 1853280, 1856400, 1884960, 1927800, 1944800, 1965600, 1969110, 2004912, 2019600, 2027025, 2042040, 2088450, 2100384, 2120580, 2162160, 2187900, 2227680, 2297295, 2316600, 2356200, 2386800, 2402400, 2423520, 2450448, 2494800, 2506140, 2552550, 2570400, 2594592, 2625480, 2650725, 2702700, 2722720, 2756754, 2784600, 2827440, 2864160, 2917200, 2948400, 3029400, 3063060, 3088800, 3132675, 3141600, 3150576, 3243240, 3281850, 3341520, 3392928, 3403400, 3500640, 3534300, 3580200, 3603600, 3675672, 3712800, 3828825, 3855600, 3938220, 4009824, 4039200, 4054050, 4084080, 4176900, 4241160, 4324320, 4375800, 4594590, 4633200, 4712400, 4773600, 4900896, 4922775, 4989600, 5012280, 5105100, 5250960, 5301450, 5405400, 5513508, 5569200, 5654880, 5834400, 5896800, 6058800, 6126120, 6265350, 6301152, 6486480, 6563700, 6683040, 6806800, 6891885, 7068600, 7160400, 7207200, 7351344, 7657650, 7711200, 7876440, 8108100, 8168160, 8353800, 8482320, 8751600, 9189180, 9266400, 9424800, 9845550, 10024560, 10210200, 10501920, 10602900, 10810800, 11027016, 11138400, 11486475, 12117600, 12252240, 12530700, 12972960, 13127400, 13613600, 13783770, 14137200, 14320800, 14702688, 15315300, 15752880, 16216200, 16707600, 16964640, 17503200, 18378360, 19691100, 20049120, 20420400, 21205800, 21621600, 22054032, 22972950, 24504480, 25061400, 26254800, 27567540, 28274400, 30630600, 31505760, 32432400, 33415200, 34459425, 36756720, 39382200, 40840800, 42411600, 44108064, 45945900, 50122800, 52509600, 55135080, 61261200, 64864800, 68918850, 73513440, 78764400, 84823200, 91891800, 100245600, 110270160, 122522400, 137837700, 157528800, 183783600, 220540320, 275675400, 367567200, 551350800, 1102701600.

1396755360: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 51, 52, 54, 55, 56, 57, 60, 63, 65, 66, 68, 70, 72, 76, 77, 78, 80, 84, 85, 88, 90, 91, 95, 96, 99, 102, 104, 105, 108, 110, 112, 114, 117, 119, 120, 126, 130, 132, 133, 135, 136, 140, 143, 144, 152, 153, 154, 156, 160, 165, 168, 170, 171, 176, 180, 182, 187, 189, 190, 195, 198, 204, 208, 209, 210, 216, 220, 221, 224, 228, 231, 234, 238, 240, 247, 252, 255, 260, 264, 266, 270, 272, 273, 280, 285, 286, 288, 297, 304, 306, 308, 312, 315, 323, 330, 336, 340, 342, 351, 352, 357, 360, 364, 374, 378, 380, 385, 390, 396, 399, 408, 416, 418, 420, 429, 432, 440, 442, 455, 456, 459, 462, 468, 476, 480, 494, 495, 504, 510, 513, 520, 528, 532, 540, 544, 546, 560, 561, 570, 572, 585, 594, 595, 608, 612, 616, 624, 627, 630, 646, 660, 663, 665, 672, 680, 684, 693, 702, 714, 715, 720, 728, 741, 748, 756, 760, 765, 770, 780, 792, 798, 816, 819, 836, 840, 855, 858, 864, 880, 884, 910, 912, 918, 924, 935, 936, 945, 952, 969, 988, 990, 1001, 1008, 1020, 1026, 1040, 1045, 1056, 1064, 1071, 1080, 1092, 1105, 1120, 1122, 1140, 1144, 1155, 1170, 1188, 1190, 1197, 1224, 1232, 1235, 1248, 1254, 1260, 1287, 1292, 1309, 1320, 1326, 1330, 1360, 1365, 1368, 1386, 1404, 1428, 1430, 1440, 1456, 1463, 1482, 1485, 1496, 1512, 1520, 1530, 1540, 1547, 1560, 1584, 1596, 1615, 1632, 1638, 1672, 1680, 1683, 1710, 1716, 1729, 1755, 1760, 1768, 1785, 1820, 1824, 1836, 1848, 1870, 1872, 1881, 1890, 1904, 1938, 1976, 1980, 1989, 1995, 2002, 2016, 2040, 2052, 2079, 2080, 2090, 2128, 2142, 2145, 2160, 2184, 2210, 2223, 2244, 2261, 2280, 2288, 2295, 2310, 2340, 2376, 2380, 2394, 2431, 2448, 2457, 2464, 2470, 2508, 2520, 2565, 2574, 2584, 2618, 2640, 2652, 2660, 2717, 2720, 2730, 2736, 2772, 2805, 2808, 2856, 2860, 2907, 2912, 2926, 2964, 2970, 2992, 3003, 3024, 3040, 3060, 3080, 3094, 3120, 3135, 3168, 3192, 3213, 3230, 3276, 3315, 3344, 3360, 3366, 3420, 3432, 3458, 3465, 3510, 3536, 3553, 3570, 3591, 3640, 3672, 3696, 3705, 3740, 3744, 3762, 3780, 3808, 3861, 3876, 3927, 3952, 3960, 3978, 3990, 4004, 4080, 4095, 4104, 4158, 4180, 4199, 4256, 4284, 4290, 4320, 4368, 4389, 4420, 4446, 4488, 4522, 4560, 4576, 4590, 4620, 4641, 4680, 4752, 4760, 4788, 4845, 4862, 4896, 4914, 4940, 5005, 5016, 5040, 5049, 5130, 5148, 5168, 5187, 5236, 5280, 5304, 5320, 5355, 5434, 5460, 5472, 5544, 5610, 5616, 5643, 5712, 5720, 5814, 5852, 5928, 5940, 5967, 5984, 5985, 6006, 6048, 6120, 6160, 6188, 6240, 6270, 6384, 6426, 6435, 6460, 6545, 6552, 6630, 6669, 6688, 6732, 6783, 6840, 6864, 6916, 6930, 7020, 7072, 7106, 7140, 7182, 7280, 7293, 7315, 7344, 7392, 7410, 7480, 7524, 7560, 7722, 7735, 7752, 7854, 7904, 7920, 7956, 7980, 8008, 8151, 8160, 8190, 8208, 8316, 8360, 8398, 8415, 8568, 8580, 8645, 8721, 8736, 8778, 8840, 8892, 8976, 9009, 9044, 9120, 9180, 9240, 9282, 9360, 9405, 9504, 9520, 9576, 9690, 9724, 9828, 9880, 9945, 10010, 10032, 10080, 10098, 10260, 10296, 10336, 10374, 10395, 10472, 10608, 10640, 10659, 10710, 10868, 10920, 11088, 11115, 11220, 11232, 11286, 11305, 11424, 11440, 11628, 11704, 11781, 11856, 11880, 11934, 11970, 12012, 12155, 12240, 12285, 12320, 12376, 12540, 12597, 12768, 12852, 12870, 12920, 13090, 13104, 13167, 13260, 13338, 13464, 13566, 13585, 13680, 13728, 13832, 13860, 13923, 14040, 14212, 14280, 14364, 14535, 14560, 14586, 14630, 14688, 14820, 14960, 15015, 15048, 15120, 15444, 15470, 15504, 15561, 15708, 15840, 15912, 15960, 16016, 16065, 16302, 16380, 16416, 16632, 16720, 16796, 16830, 17017, 17136, 17160, 17290, 17442, 17556, 17680, 17765, 17784, 17952, 17955, 18018, 18088, 18360, 18480, 18564, 18720, 18810, 19019, 19040, 19152, 19305, 19380, 19448, 19635, 19656, 19760, 19890, 20020, 20064, 20196, 20349, 20520, 20592, 20748, 20790, 20944, 20995, 21216, 21280, 21318, 21420, 21736, 21840, 21879, 21945, 22176, 22230, 22440, 22572, 22610, 22880, 23205, 23256, 23408, 23562, 23712, 23760, 23868, 23940, 24024, 24310, 24453, 24480, 24570, 24752, 24871, 25080, 25194, 25245, 25704, 25740, 25840, 25935, 26180, 26208, 26334, 26520, 26676, 26928, 27027, 27132, 27170, 27360, 27664, 27720, 27846, 28080, 28215, 28424, 28560, 28728, 29070, 29172, 29260, 29393, 29640, 29835, 29920, 30030, 30096, 30240, 30888, 30940, 31008, 31122, 31416, 31824, 31920, 31977, 32032, 32130, 32604, 32760, 33264, 33345, 33440, 33592, 33660, 33915, 34034, 34272, 34320, 34580, 34884, 35112, 35343, 35360, 35530, 35568, 35910, 36036, 36176, 36465, 36720, 36960, 37128, 37620, 37791, 38038, 38304, 38610, 38760, 38896, 39270, 39312, 39501, 39520, 39780, 40040, 40392, 40698, 40755, 41040, 41184, 41496, 41580, 41769, 41888, 41990, 42636, 42840, 43472, 43605, 43680, 43758, 43890, 44460, 44880, 45045, 45144, 45220, 46189, 46410, 46512, 46683, 46816, 47124, 47520, 47736, 47880, 48048, 48620, 48906, 49140, 49504, 49742, 50160, 50388, 50490, 51051, 51408, 51480, 51680, 51870, 52360, 52668, 53040, 53295, 53352, 53856, 54054, 54264, 54340, 55328, 55440, 55692, 56160, 56430, 56848, 57057, 57120, 57456, 58140, 58344, 58520, 58786, 58905, 59280, 59670, 60060, 60192, 61047, 61776, 61880, 62244, 62832, 62985, 63648, 63840, 63954, 64260, 65208, 65520, 65637, 65835, 66528, 66690, 67184, 67320, 67830, 68068, 68640, 69160, 69615, 69768, 70224, 70686, 71060, 71136, 71820, 72072, 72352, 72930, 73359, 73440, 74256, 74613, 75240, 75582, 76076, 77220, 77520, 77792, 77805, 78540, 78624, 79002, 79560, 80080, 80784, 81396, 81510, 82080, 82992, 83160, 83538, 83980, 85085, 85272, 85680, 86944, 87210, 87516, 87780, 88179, 88920, 89760, 90090, 90288, 90440, 92378, 92820, 93024, 93366, 94248, 95095, 95472, 95760, 95931, 96096, 97240, 97812, 98280, 99484, 100320, 100776, 100980, 101745, 102102, 102816, 102960, 103740, 104720, 105336, 106080, 106590, 106704, 108108, 108528, 108680, 109395, 110880, 111384, 112860, 113373, 113696, 114114, 114912, 116280, 116688, 117040, 117572, 117810, 118560, 119340, 120120, 122094, 122265, 123552, 123760, 124355, 124488, 125664, 125970, 127908, 128520, 130416, 131040, 131274, 131670, 133380, 134368, 134640, 135135, 135660, 136136, 138320, 138567, 139230, 139536, 140448, 141372, 142120, 143640, 144144, 145860, 146718, 146965, 148512, 149226, 150480, 151164, 152152, 153153, 154440, 155040, 155610, 157080, 158004, 159120, 159885, 160160, 161568, 162792, 163020, 165984, 166320, 167076, 167960, 170170, 170544, 171171, 171360, 174420, 175032, 175560, 176358, 176715, 177840, 180180, 180576, 180880, 184756, 185640, 186732, 188496, 188955, 190190, 190944, 191520, 191862, 194480, 195624, 196560, 197505, 198968, 201552, 201960, 203490, 204204, 205920, 207480, 208845, 209440, 210672, 213180, 213408, 216216, 217056, 217360, 218790, 222768, 223839, 225720, 226746, 228228, 230945, 232560, 233376, 233415, 234080, 235144, 235620, 238680, 240240, 244188, 244530, 247520, 248710, 248976, 251940, 255255, 255816, 257040, 260832, 262548, 263340, 264537, 266760, 269280, 270270, 271320, 272272, 276640, 277134, 278460, 279072, 282744, 284240, 285285, 287280, 288288, 291720, 293436, 293930, 298452, 300960, 302328, 304304, 305235, 306306, 308880, 311220, 314160, 316008, 318240, 319770, 323323, 325584, 326040, 328185, 332640, 334152, 335920, 340340, 341088, 342342, 348840, 350064, 351120, 352716, 353430, 355680, 360360, 361760, 366795, 369512, 371280, 373065, 373464, 376992, 377910, 380380, 383724, 388960, 391248, 393120, 395010, 397936, 403104, 403920, 406980, 408408, 414960, 415701, 417690, 421344, 426360, 432432, 434720, 437580, 440895, 445536, 447678, 451440, 453492, 456456, 459459, 461890, 465120, 466830, 470288, 471240, 477360, 479655, 480480, 488376, 489060, 497420, 497952, 503880, 510510, 511632, 513513, 514080, 525096, 526680, 529074, 533520, 540540, 542640, 544544, 554268, 556920, 565488, 566865, 568480, 570570, 574560, 583440, 586872, 587860, 596904, 604656, 608608, 610470, 612612, 617760, 622440, 628320, 632016, 639540, 646646, 651168, 652080, 656370, 668304, 671517, 671840, 680680, 684684, 692835, 697680, 700128, 702240, 705432, 706860, 720720, 733590, 739024, 742560, 746130, 746928, 755820, 760760, 765765, 767448, 782496, 790020, 793611, 795872, 807840, 813960, 816816, 829920, 831402, 835380, 852720, 855855, 864864, 875160, 881790, 895356, 902880, 906984, 912912, 918918, 923780, 933660, 940576, 942480, 954720, 959310, 969969, 976752, 978120, 994840, 1007760, 1021020, 1023264, 1027026, 1050192, 1053360, 1058148, 1067040, 1081080, 1085280, 1108536, 1113840, 1119195, 1130976, 1133730, 1141140, 1166880, 1173744, 1175720, 1193808, 1209312, 1220940, 1225224, 1244880, 1247103, 1264032, 1279080, 1293292, 1304160, 1312740, 1322685, 1336608, 1343034, 1361360, 1369368, 1385670, 1395360, 1410864, 1413720, 1441440, 1467180, 1478048, 1492260, 1493856, 1511640, 1521520, 1531530, 1534896, 1580040, 1587222, 1616615, 1627920, 1633632, 1662804, 1670760, 1705440, 1711710, 1750320, 1763580, 1790712, 1813968, 1825824, 1837836, 1847560, 1867320, 1884960, 1918620, 1939938, 1953504, 1956240, 1989680, 2015520, 2042040, 2054052, 2078505, 2100384, 2106720, 2116296, 2162160, 2217072, 2227680, 2238390, 2267460, 2282280, 2297295, 2347488, 2351440, 2387616, 2441880, 2450448, 2489760, 2494206, 2558160, 2567565, 2586584, 2625480, 2645370, 2686068, 2722720, 2738736, 2771340, 2821728, 2827440, 2909907, 2934360, 2984520, 3023280, 3043040, 3063060, 3069792, 3160080, 3174444, 3233230, 3255840, 3325608, 3341520, 3357585, 3423420, 3500640, 3527160, 3581424, 3627936, 3675672, 3695120, 3734640, 3837240, 3879876, 3912480, 3968055, 3979360, 4084080, 4108104, 4157010, 4232592, 4324320, 4434144, 4476780, 4534920, 4564560, 4594590, 4702880, 4849845, 4883760, 4900896, 4988412, 5116320, 5135130, 5173168, 5250960, 5290740, 5372136, 5477472, 5542680, 5654880, 5819814, 5868720, 5969040, 6046560, 6126120, 6235515, 6320160, 6348888, 6466460, 6651216, 6683040, 6715170, 6846840, 7054320, 7162848, 7351344, 7390240, 7469280, 7674480, 7759752, 7936110, 8168160, 8216208, 8314020, 8465184, 8729721, 8953560, 9069840, 9129120, 9189180, 9699690, 9767520, 9976824, 10270260, 10346336, 10501920, 10581480, 10744272, 11085360, 11639628, 11737440, 11938080, 12252240, 12471030, 12697776, 12932920, 13302432, 13430340, 13693680, 14108640, 14549535, 14702688, 15348960, 15519504, 15872220, 16432416, 16628040, 17459442, 17907120, 18139680, 18378360, 19399380, 19953648, 20540520, 21162960, 21488544, 22170720, 23279256, 24504480, 24942060, 25395552, 25865840, 26860680, 27387360, 29099070, 31039008, 31744440, 33256080, 34918884, 35814240, 36756720, 38798760, 39907296, 41081040, 42325920, 43648605, 46558512, 49884120, 51731680, 53721360, 58198140, 63488880, 66512160, 69837768, 73513440, 77597520, 82162080, 87297210, 93117024, 99768240, 107442720, 116396280, 126977760, 139675536, 155195040, 174594420, 199536480, 232792560, 279351072, 349188840, 465585120, 698377680, 1396755360.

etc.

Updated: 2018-DEC-15.

Prime Numbers Background:

This research is based off a posting I made a year ago about prime numbers and prime factorizations. At that same time, I was also exploring highly composite numbers.

Prime vs. Composite Numbers:

One way to think about prime vs. composite numbers is the following:

• prime numbers = the atoms of numbers
• composite numbers = the molecules of numbers

Performance / Application Versions:

Highly Composite Numbers v0.3

• v0.1: November 14th, 2017:
• A quick C# application and about an hour's worth of runtime shows the first results, up to 554,400.
• v0.2: December 7th, 2018:
• I improved my program significantly with a fiew optimizations, and could reproduce the previous hours' work in 15 seconds.
• The main optimzation was to only search up until the square root of the number being factored, and pull out both factors. Such as, factoring 100 into 2 also gives you 50, and you only have to go as far as 10 -- the square root of 100. Note that 10 also gives you another 10, as 10 * 10 = 100, which you must ignore to avoid duplicate factors.
• v0.3: December 8th, 2018:
• "Graphical" and HTML output improvements, to help me blog the results.
• Left it running over the Christmas holidays for about 2 weeks and got results up until 1,396,755,360!

More Optimzations?

• Looking forward, I wish to get into multi-threading, it is something I have not coded for a long time. Not even our games were multi-threaded (to maintian simplicity), although they were highly optimized. The last time I coded multi-threaded algorigthms -- from memory -- was eScape. And that was in C++, helped by Jason Doucette.
• Using prime factors:
• As explained in the "5040 and other Anti-Prime Nubmers - Numberphile" video below, I could use the patterns found within the constructions of HCNs to create them, with some math logic (that I have not figured out yet) to ensure I do not miss any. This will be an insane optimzation and will likely complete 2 weeks of v0.3's work in a matter of seconds.

Videos:

5040 and other Anti-Prime Nubmers - Numberphile

More: