Subsets of colossally abundant numbers

Abstract

Let $G(n)=\sigma (n)/(n\log \log n)$. Robin made hypothesis that $G(n)<e^{\gamma }$ for all integer $n>5040$. This article divides all colossally abundant numbers in to three disjoint subsets CA1, CA2 and CA3, and shows that Robin hypothesis is true if and only if all CA2 numbers $n>5040$ satisfy Robin inequality.

23 pages