  We 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 $c(n,r)$.
