On the ratio between two factorization functions
Volume 213 / 2024
Acta Arithmetica 213 (2024), 379-386
MSC: Primary 11A51; Secondary 11N37
DOI: 10.4064/aa230613-31-12
Published online: 5 February 2024
Abstract
Let $f(n)$ be the number of factorizations of $n$, i.e., representations of $n$ as an unordered product of integers greater than $1$. In addition, let $F(n)$ be the number of factorizations of $n$ into distinct parts. In this note, we provide a new upper bound for the ratio $f(n)/F(n)$.
