On the Oppenheim's "factorisatio numerorum" function

TL;DR

This paper investigates the properties of the function counting the number of distinct unordered factorizations of natural numbers into factors greater than one.

Contribution

It explores new aspects of the factorization counting function, providing insights into its behavior and properties.

Findings

Analysis of the growth rate of f(n)

Characterization of the distribution of factorizations

Identification of special cases and patterns

Abstract

Let $f(n)$ denote the number of distinct unordered factorisations of the natural number $n$ into factors larger than 1.In this paper, we address some aspects of the function $f(n)$.