A generalization of the Smarandache function
نویسنده
چکیده
For any positive integer n, we define the function P (n) as the smallest prime p such that n | p!. That is, P (n) = min{p : n |p!, where p be a prime}. This function is a generalization of the famous Smarandache function S(n). The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of P (n), and give two interesting mean value formulas for it.
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