On the mean value of the Pseudo-Smarandache function
نویسنده
چکیده
For any positive integer n, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer k such that n | k(k + 1) 2 . That is, Z(n) = min { k : n| + 1) 2 } . The main purpose of this paper is using the elementary methods to study the mean value properties of p(n) Z(n) , and give a sharper asymptotic formula for it, where p(n) denotes the smallest prime divisor of n.
منابع مشابه
On the mean value of the Pseudo-Smarandache-Squarefree function
For any positive integer n, the Pseudo Smarandache Squarefree function Zw(n) is defined as Zw(n) = min{m : n|mn, m ∈ N}, and the function Z(n) is defined as Z(n) = min { m : n ≤ m(m + 1) 2 , m ∈ N } . The main purpose of this paper is using the elementary methods to study the mean value properties of the function Zw(Z(n)), and give a sharper mean value formula for it.
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