On the Least counterexample to Robin hypothesis

TL;DR

This paper investigates the properties and requirements of the smallest counterexample to Robin's hypothesis, which relates to the inequality involving the sum of divisors function and the Euler-Mascheroni constant.

Contribution

It systematically identifies the necessary conditions that the least counterexample to Robin's hypothesis must fulfill.

Findings

Outlines the properties that the least counterexample must satisfy

Provides a framework for identifying potential counterexamples

Contributes to understanding the structure of possible violations of Robin's hypothesis

Abstract

Let $G(n)=\sigma (n)/(n \log \log n )$. Robin made hypothesis that $G(n)<e^\gamma$ for all integer $n>5040$. If Robin hypothesis fails, there will be a least counterexample. This article collects the requirements the least counterexample should satisfy.