Research Article Open Access

On Sum of Divisors and Robin’s Theorem

Abstract

A result of Robin states that if the Riemann Hypothesis fails then the sum of divisors function is greater than for infinitely many , where is Euler’s constant. We show in this paper this happens only for values of n less than a certain threshold. We do this by identifying convenient expressions for , and using the value of these expressions to perform induction on the form of the prime factorization for . We find by this method that all values of σ for which are necessarily less than n=25×33×53 ×72.

Valentin B. Bura