一个包含Smarandache LCM对偶函数的方程

An equation involving the Smarandache LCM dual function

对任意正整数n,定义两个Smarandache LCM函数的对偶函数SL*(n)=max{k:k∈N,[1,2,…,k]|n}和S*(n)=max{m:m∈N,m!|n}.用初等方法研究函数方程∑d|nSL*(d)=∑d|nS*(d)的可解性,并获得了该方程的所有正整数解。

For any positive integer n, dual functions of two Smarandache LCM function are defined by SL^＊ （n）max{k：k∈N,[1,2,…,k]｜n}andS^＊（n）=max{m：m∈N,m!｜n}.By using the elementary method,the solvability of the equation ∑d｜nSL^＊（d）=∑d｜nS^＊（d） are studied, and all positive integer solutions of this equation are obtained.