Euler-type Recurrence Relation for Arbitrary Arithmetical Function
Number Theory
2025-10-03 v1 Combinatorics
Abstract
An interplay between the Lambert series and Euler's Pentagonal Number Theorem gives an Euler-type recurrence relation for any given arithmetical function. As consequences of this, we present Euler-type recurrence relations for some well-known arithmetic functions. Furthermore, we derive Euler-type recurrence relations for certain partition functions and sum-of-divisors functions using infinite product identities of Jacobi and Gauss.
Keywords
Cite
@article{arxiv.2510.01277,
title = {Euler-type Recurrence Relation for Arbitrary Arithmetical Function},
author = {A. David christopher},
journal= {arXiv preprint arXiv:2510.01277},
year = {2025}
}