Signed harmonic sums of integers with $k$ distinct prime factors

TL;DR

This paper explores harmonic sums involving integers with a fixed number of prime factors, providing both theoretical insights and computational results on their properties.

Contribution

It introduces new theoretical and computational analyses of harmonic sums over integers with a specified number of prime factors.

Findings

Identification of properties of harmonic sums with prime factors

Computational results supporting theoretical conjectures

Insights into the distribution of such harmonic sums

Abstract

We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.