：对任意的正整数n，伪Smarandache函数Z（n）定义为最小的正整数m使得n| m(m+1)/2，即Z（n）=min {m ： n| m(m+1)/2,m∈N}。而伪Smarandache无平方因子函数Z（w n）定义为最小的正整数m使得n| mn ，即Zw（n）= min{m ： n| m } n,m ∈N 。利用初等和解析的方法研究了伪Smarandache函数Z（n）与伪Smarandache无平方因子函数 Zw（n）的混合均值问题，并获得一个较强的渐近公式。%For any positive integer n,the famous Pseudo-Smarandache function Z(n)is defined as the smallest positive integer m such that n|m(m+1)/2 . That is,Z(n)= min {m : n|m(m+1)/2,m∈N} .While Pseudo-Smarandache- Squarefree function Zw (n)is defined as Zw (n)= min {m : n| m } n,m ∈N . Using the elementary and analytic method we study the hybrid mean value problem invoving the Pseudo-Smarandache function Z(n)and Pseudo-Smarandache- Squarefree function,and give a shaper asymptotic formula for it.
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