  Ramanujan sums have been studied and generalized by several authors. For
example, Nowak studied these sums over quadratic number fields, and Grytczuk
defined that on semigroups. In this note, we deduce some properties on sums of
generalized Ramanujan sums and give examples on number fields. In particular,
we have a relational expression between Ramanujan sums and residues of Dedekind
zeta functions.
