对任意正整数n，著名的Smarandache 对偶函数S*(n)定义为使得m!|n最大的正整数m.利用初等方法研究了一类包含Smarandache对偶函数方程∑d|nS*(d)=n的可解性,并获得了该方程的所有正整数解，其解为1和12．

For any positive integer n, the famous Smarandache dual function S*(n) is defined as the greatest positive integer m such that m! divides n. The main purpose of this paper is to study the solutions of the equation ∑d|nS*(d)=n by using the elementary method and to obtain all its positive integer solutions which ane proved to be 1 and 12.