关于Smarandache Ceil函数的一个混合均值

On a Hybrid Mean Value of the Smarandache Ceil Function

对任意正整数n,k≥2为给定整数,Smarandache Ceil函数sk(n)定义为最小的正整数x,使得n|xk,即Sk(n)=min{x∶x∈N,n|xk}.利用Smarandache Ceil函数的定义及解析的方法,研究Smarandache Cei函数sk(n)与欧拉函数的均值分布性质,并给出一个有趣的渐近公式.

For any positive integer nand the given positive integer k（k≥2）,he Smarandache Ceil function sk（n）is defined as the smallest positive integerx which makes n｜xk,that is Sk（n）=min{x∶x∈N,n｜ xk}.The definition and the analytic method of the Smarandache Ceil function was utilized to study the distribution properties of the mean value of sk（n）and the Euler function,and give an interesting asymptotic formula.