关于Smarandache函数的复合函数的均值

On the Mean Value of the Smarandache Function

对任意的正整数n,定义数论函数W(n)为最小的正整数k,使得n≤k(3k+1),即W(n)=min{k:n≤k(3k+1),k∈N}.利用初等及解析的方法研究复合函数S(W(n))的均值分布,并获得了较强的均值分布的渐近公式.

For any positive integer n, the new function W（n） is defined as the smallest positive integer k such that n≤k（3k＋1）. That is W（n）=min W（n）=min{k：n≤k（3k＋1）,k∈N}.. The main purpose of this paper is to study the mean value properties of the composite function S （V/（n））, and to give a sharper asymptotic formula by the elementary and analytic method.