Subsets of colossally abundant numbers

2019/03/08 by Xiaolong Wu, Wu, Xiaolong
Mathematics · #11A25 11A41 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11A41

paper · pdf · doi:10.48550/arxiv.1903.03490

23 pages

arxiv created 2019/03/08 · openalex publication_date 2019/03/08 · arxiv updated 2019/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G(n)=σ(n)/(n log log n ). Robin made hypothesis that G(n)<e^γ 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.

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