A Note on f-Minimum Functions

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


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
URI https://vuir.vu.edu.au/id/eprint/17588
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords divisibility of integers, prime factorization, arithmetical functions, perfect numbers
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