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December 2008 Quelques inégalités effectives entre des fonctions arithmétiques usuelles
Jean-Louis Nicolas
Funct. Approx. Comment. Math. 39(2): 315-334 (December 2008). DOI: 10.7169/facm/1229696578

Abstract

Let us denote by $\tau(n)$ and $\sigma(n)$ the number and the sum of the divisors of $n$ and by $\varphi$ Euler's function. We give effective upper bounds for $\frac{n}{\varphi(n)}$ in terms of $\varphi(n)$, and for $\frac{\sigma(n)}{n}$ in terms of $\tau(n)$.

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Jean-Louis Nicolas. "Quelques inégalités effectives entre des fonctions arithmétiques usuelles." Funct. Approx. Comment. Math. 39 (2) 315 - 334, December 2008. https://doi.org/10.7169/facm/1229696578

Information

Published: December 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1232.11100
MathSciNet: MR2490743
Digital Object Identifier: 10.7169/facm/1229696578

Subjects:
Primary: 11N56

Rights: Copyright © 2008 Adam Mickiewicz University

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Vol.39 • No. 2 • December 2008
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