关于Smarandache函数S(n)与除数函数d(n)的混合均值

On the hybrid mean value of the Smarandache function and the Dirichlet divisor function

对于任意的正整数n,著名的Smarandache函数S(n)定义为最小的正整数m,使得n|m!,即就是S(n)=min{m:n|m!,m∈N}.本文的主要目的是应用初等方法研究S(n)与除数函数d(n)的加权均值问题,并获得一个有趣的渐进公式.

For any positive integer n, the Smarandache function S（n） defined as the smallest positive integer m such that n｜m! . That is, S（n） = min{m ： n｜m!, m ∈ N}. The main purpose of the paper is using the elementary methods to study the hybrid mean value problem involving the Smarandache function and the Dirichlet divisor function, and to give a sharper asymptotic formula for it.