The hybrid mean value of the Smarandache function and the Mangoldt function

Abstract

For any positive integer n, the famous F.Smarandache function S(n) is deflned as the smallest positive integer m such that njm!. The main purpose of this paper is using the elementary methods to study the hybrid mean value of the Smarandache function S(n) and the Mangoldt function ⁄(n), and prove an interesting hybrid mean value formula for