Mean-value estimations for the Möbius function I

A weighted Möbius function

Computing the Summation of the Möbius Function

Mean value of a Smarandache-Type Function

In this paper, we use analytic method to study the mean value properties of Smarandache-Type Multiplicative Functions Km(n), and give its asymptotic formula. Finally, the convolution method is used to improve the error term. Suppose m ≥ 2 is a fixed positive integer. If n = p α1 1 p α2 2 ...p α k k , we define K m (n) = p β1 1 p β2 which is a Smarandache-type multiplicative function. Yang Cundi...

Mean value of F. Smarandache LCM function

Abstract For any positive integer n, the famous Smarandache function S(n) defined as the smallest positive integer m such that n | m!. That is, S(n) = min{m : n | m!, n ∈ N}. The Smarandache LCM function SL(n) the smallest positive integer k such that n | [1, 2, · · · , k], where [1, 2, · · · , k] denotes the least common multiple of 1, 2, · · · , k. The main purpose of this paper is using the ...

Posets with maximal Möbius function

The absolute value of the Möbius function of a bounded poset P with n + 2 elements satisfies |μ(P )| ≤ max r≥0 max p1+...+pr=n pi≥1 r ∏