A Divisor Function Inequality

TL;DR

This paper improves an existing upper bound for the sum of divisors function using elementary techniques, contributing to the understanding of divisor sums and their relation to prime distribution.

Contribution

It presents a sharper upper bound for a classical divisor function inequality using elementary methods, advancing pure mathematical knowledge.

Findings

Established a new, tighter upper bound for the sum of divisors function.

Demonstrated the effectiveness of elementary techniques in deriving bounds.

Contributed to the theoretical understanding of divisor sums and prime distribution.

Abstract

This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely elementary.