Integer Sequence Approved by OEIS

Friday, August 7, 2020
By: Matthew Doucette

An integer sequence I discovered in 2019 was approved today by OEIS -- The On-Line Encyclodpedia of Integer Sequences!

 

Definition:

This is the technical definition of the sequence:

https://oeis.org/A332271

A332271: a(n) is the smallest positive integer that is not a divisor of the n-th highly composite number (A002182).

What it means:

For all highly composite numbers (numbers that are the most divisible which are numbers that have more factors than any number before it), what is the first factor when counting up from 1 that is skipped or missed (what is the smallest or least factor)?

In other words, for numbers that are the most divisible (numbers with the most factors), which factors tend to be the first ones missed or skipped. Interestingly, they correlate to prime numbers often, but not always.

 

Original Article:

Our original post is Lowest Unused Anti-Prime (Highly Composite Number) Factors.

 

See Also:

See more of our math theory work.

 

That is all.

 

 

About the Author: I am Matthew Doucette of Xona Games, an award-winning indie game studio that I founded with my twin brother. We make intensified arcade-style retro games. Our business, our games, our technology, and we as competitive gamers have won prestigious awards and received worldwide press. Our business has won $180,000 in contests. Our games have ranked from #1 in Canada to #1 in Japan, have become #1 best sellers in multiple countries, have won game contests, and have held 3 of the top 5 rated spots in Japan of all Xbox LIVE indie games. Our game engines have been awarded for technical excellence. And we, the developers, have placed #1 in competitive gaming competitions -- relating to the games we make. Read about our story, our awards, our games, and view our blog.