一个包含Smarandache函数的混合均值

A Hybrid Mean Value Formula Involing Smarandache Function

对任意n∈N+,著名的F.Smarandache LCM函数SL(n)定义为最小的正整数k使得n|[1,2,…,k],即SL(n)=min{k:n|[1,2,…,k]}。本文利用初等和解析的方法研究了SmarandacheLCM函数SL(n)和除数函数σ(n)的混合均值,并给出了一个较强的渐近公式。

For any positive integer n, the famous F. Smarandache LCM function SL （n） is defined as the smallest positive integer k such that n｜[1,2,…,k] That is, SL（n）=min{k：n｜[1,2,…,k]}. The elementary and analyti- cal methods are used to study the hybrid mean value formula involing Smarandache function and the Dirichlet divi- sor function, and a sharp asymptotic formula is given for it.