关于Smarandache LCM函数对偶函数的方程

On the Equation of the Smarandache Dual LCM Function

对于任意的正整数n,著名的Smarandache LCM函数的对偶函数SL*(n)=max{k∶[1,2,…,k]|k,k∈N},ω(n)表示n的不同素因子的个数.利用初等数论和分析的方法研究函数方程∏d|nSL*(d)+1=2ω(n)的可解性,并得到了该方程的所有正整数解.

For any positive integer n,the dual function of the well-known Smarandache LCM function is defined by SSL＊（n）=max{k：[1,2,…,k]｜k∈N）,where w（n） is all the different prime factor numbers of n. By using the elementary number theory and analytic methods, the solvability of the equation Π（d｜n）SL＊（d）＋1=2w（n） is studied,and all its positive integer solutions of this equation are obtained.