On the Pseudo-smarandache Squarefree Function
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چکیده
In this paper we discuss various problems and conjectures concered the pseudo-Smarandache squarefree function.
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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This function generalizes many particular functions. For f( k) = k! one gets the Smarandache function, while for f(k) = k(k: 1) one has the Pseudo-Smarandache function Z (see [1], [4-5]). In the above paper [3] we have defined also dual arithmetic functions as follows: Let 9 : N* -+ N* be a function having the property that for each n 2:: 1 there exists at least a k 2:: 1 such that g(k)ln. Let ...
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