2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106136We study equations of the form $σ(p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. We shall improve upper bounds for the size and the number of solutions of such equations.14 pages, submitted to Math. Proc. Cambridge Phil. SocNumber Theory11A05(Primary) 11A25, 11D61(Secondary)text