关于Smarandache LCM函数对偶函数的方程

摘要

For any positive integer, the well-known dual function of Smarandache LCM function is defined by SL ＊ = maxt SL（n）=max{k：[1,2,…,k]｜K,K∈N} is all the different prime factor numbers of n. By using the elementary number theory and analysis methods, the solvability of the equation SL（d）＋1=2^ω（n） is studied, and all its positive integer solutions of this equation are obtained.%摘要：对于任意的正整数n，著名的SmarandacheLCM函数的对偶函数SL（n）=max｛k：[1，2，…，k]｜K,K∈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SL（d）＋1=2^ω（n）的可解性，并获得了该方程的所有正整数解．