一个特殊数论函数的均值(英文)

On the Mean Value of a Special Function

研究由两个Smarandache函数构成的一个特殊数论函数。应用初等方法来研究序列1/(sK(n))ep(n),并给出一个它的渐进公式。

For any fixed positive integer k 〉 1 and any positive integer n, let Sk （n）—— denotes the largest positive integer m satisfying m^k │ n, and for any fixed prime p, let ep （n） denotes the largest nonnegative integer α satisfying p^a│n ,the elementary properties of sequences （sk（n））^ep（n）-- ----1 is studied with elementary method and an interesting asymptotic formula for it is given.