Quelques inégalités effectives entre des fonctions arithmétiques usuelles

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 $\tau(n)$.