关于不同因子分解的数目

On the Number of Essentially Different Factorizations of a Positive Integer

设f(n)表示分解自然数n(＞ 1)为大于1的整数因子乘积的所有方式的数目(不计因子的顺序),并设0＜β＜1,N(x,β)=Card{n≤x,f(n)≥nβ}.本文分别估计了N(x,β)和f(n)的值.

Let f(n) denote the number of factorizations of the natural number n into factors larger than 1, where the order of the factors does not count, and N(x, β)-Card{n≤ x,f(n)≥nβ},0<β< 1. In this paper, the estimates for N(x,β) and the values of f(n) are given.