2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212091Let us denote by $τ(n)$ and $\si(n)$ the number and the sum of the divisors of $n$ and by $\vfi$ Euler's function. We give effective upper bounds for $\frac{n}{\vfi(n)}$ in terms of $\vfi(n)$, and for $\frac{\si(n)}{n}$ in terms of $τ(n)$.Number Theorytext