2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157638We study certain step functions whose nonnegativity is related to the integrality of sequences of ratios of factorial products. In particular, we obtain a lower bound for the mean square of such step functions which allows us to give a restriction on when such a factorial ratio sequence can be integral. Additionally, we note that this work has applications to the classification of cyclic quotient singularities.11 Pages; argument improved and simplified; references addedNumber Theorytext