On the Number of Multiplicative Partitions

Cao Hui-Zhong1
1Department of Mathematics Shandong University Jinan, Shandong China

Abstract

Let \(f(n)\) denote the number of essentially different factorizations of \(n\). In this paper, we prove that for every odd number \( > 1\), we have \(f(n) \leq c\frac{n}{\log n},\) where \(c\) is a positive constant.