中文摘要：

利用初等数论和解析数论的方法研究著名的Smarandache幂函数SP(n)的均值估计问题.首先给出Smarandache幂函数SP(n)的定义,几个重要的性质和相关引理.在此基础上得到了一些有意义的结果,即在简单数序列上得到了∑n∈A n≤x1/S(SP(n))和∑n∈A n≤x S(SP(n))的均值.

英文摘要：

Using elementary number theory and methods of analytic number theory to study the problem of the mean estimate of the famous Smarandache power function SP (n).First the def-inition and several important properties of Smarandache power function SP (n)were given,then based on several related lemma,some meaningful results were obtained that is the mean value of ∑n∈A n ≤x 1 S(SP (n))and ∑n∈A n ≤x S (SP (n))on the simple number sequences.