General Mathematics

    

A Note on F-Minimum Functions

Authors: Jozsef Sandor

For a given arithmetical function f : N ! N, let F : N ! N be de¯ned byF(n) = minfm ¸ 1 : njf(m)g, if this exists. Such functions, introduced in [4], will be called as the f-minimum functions. If f satis¯es the property a · b =) f(a)jf(b), we shall prove that F(ab) = maxfF(a); F(b)g for (a; b) = 1. For a more restrictive class of functions, we will determine F(n) where n is an even perfect number. These results are generalizations of theorems from [10], [1], [3], [6].

Comments: 4 Pages.

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[v1] 2014-03-14 06:34:11

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