2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/117919We prove a simple formula for the main value of $r$-even functions and give applications of it. Considering the generalized Ramanujan sums $c_A(n,r)$ involving regular systems $A$ of divisors we show that it is not possible to develop a Fourier theory with respect to $c_A(n,r)$, like in the the usual case of classical Ramanujan sums $c(n,r)$.Number Theory11A25, 11L03, 11N37text