The generating function of the $\sigma_1$ function

TL;DR

This paper derives a generating function for the sum-of-divisors function σ₁ and explores its connections to Ramanujan's tau function, aiming to shed light on unresolved problems in classical number theory.

Contribution

It introduces a new generating function for σ₁ and investigates its relationship with Ramanujan's tau function, providing potential insights into longstanding number theory problems.

Findings

Derived a generating function for σ₁

Identified connections between σ₁ and Ramanujan's tau function

Proposed implications for unsolved number theory problems

Abstract

In this paper, we give a generate function for the $\sigma_1$ function. Then we find some connections between the $\sigma_1$ function and the Ramanujan's tau function. We hope this connection will give some insights into the unsolved problems in classical number theory.