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 $\tau(n)$.
Citation
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
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