两个数论函数的混合均值

Hybrid Mean Value on the Two Number Theory Functions

任意n∈N＋,著名的F.SmarandacheLCM函数SL（n）定义为最小的正整数k使得n｜[1,2,…,k],即就是SL（n）=min{k：n｜[1,2,…,k]}。利用初等的方法研究了SmarandacheLCM函数SL（n）与Mangoldt函数Λ（n）的混合均值问题,并给出了一个较强的渐进公式。

For any positive integer n,the famous F.Smarandache LCM function SL（n）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 methods is used to study the hybrid mean value involving the F.Smarandache function and the Mangoldt function,and a sharp asymptotic formula is given for it.