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December 2009 On the composition of a certain arithmetic function
Florian Luca, József Sándor
Funct. Approx. Comment. Math. 41(2): 185-209 (December 2009). DOI: 10.7169/facm/1261157809

Abstract

Let $S(n)$ be the function which associates for each positive integer $n$ the smallest positive integer $k$ such that $n\mid k!$. In this note, we look at various inequalities involving the composition of the function $S(n)$ with other standard arithmetic functions such as the Euler function and the sum of divisors function. We also look at the values of $S(F_n)$ and $S(L_n)$, where $F_n$ and $L_n$ are the $n$th Fibonacci and Lucas numbers, respectively.

Citation

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Florian Luca. József Sándor. "On the composition of a certain arithmetic function." Funct. Approx. Comment. Math. 41 (2) 185 - 209, December 2009. https://doi.org/10.7169/facm/1261157809

Information

Published: December 2009
First available in Project Euclid: 18 December 2009

zbMATH: 1252.11004
MathSciNet: MR2590333
Digital Object Identifier: 10.7169/facm/1261157809

Subjects:
Primary: 11A25
Secondary: 11B39, 11N37, 11N56

Rights: Copyright © 2009 Adam Mickiewicz University

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Vol.41 • No. 2 • December 2009
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