Inductive Formulas for some Arithmetic Functions

TL;DR

This paper develops recursive formulas and identities connecting sums of divisors, triangular numbers, and divisor functions, offering new inductive methods for analyzing arithmetic functions.

Contribution

It introduces novel recursive formulas and identities linking various arithmetic functions and divisor sums, expanding the toolkit for their analysis.

Findings

Derived recursive formulas for sums of divisors and triangular numbers.

Established identities relating arithmetic functions to divisor functions.

Provided inductive identities for analyzing arithmetic functions.

Abstract

We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.