2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74814We answer a number of questions relating to the pseudo-Smarandache function Z(n). We show that the ratio of consecutive values $Z(n+1)/Z(n)$ and $Z(n-1)/Z(n)$ are unbounded; that $Z(2n)/Z(n)$ is unbounded; that $n/Z(n)$ takes every integer value infinitely often; and that the series $\sum_n 1/Z(n)^α$ is convergent for any $α> 1$.Number Theory11A25; 11B83text