Pseudo-Smarandache-Squarefree函数及其它的均值

Pseudo-Smarandache-Squarefree Function and Its Value Distribution

对于任意正整数n,Pseudo-Smarandache-Squarefree函数Zw(n)定义为Zw(n)=min{m:n|mn,m∈N}.应用初等方法研究Zw(n)的值的分布性质,并给出两个较强的渐进公式.

For any positive integer n, the Pseudo - Smarandache - Squarefree function Zw （n） is Zw （n） = min（ m ：n｜mn ,m ∈ N）. The main purpose of the paper is to study the arithmetical properties of Zw （n） by the elementary methods, and to offer two sharper asymptotic formulae for it.