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A Note on f-Minimum Functions

Sándor, József (2007) A Note on f-Minimum Functions. Research report collection, 10 (2).

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Abstract

For a given arithmetical function f : N → N, let F : N → N be defined by F(n) = min{m ≥ 1 : n|f(m)}, if this exists. Such functions, introduced in [4], will be called as the f-minimum functions. If f satisfies the property a ≤ b → f(a)|f(b), we shall prove that F(ab) = max{F(a), F(b)} for (a, b) = 1. For a more restrictive class of functions, we will determine F(n) where n is an even perfect number.

Item Type: Article
Uncontrolled Keywords: divisibility of integers, prime factorization, arithmetical functions, perfect numbers
Subjects: FOR Classification > 0101 Pure Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 11 Feb 2012 04:43
Last Modified: 23 May 2013 16:51
URI: http://vuir.vu.edu.au/id/eprint/17588
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