, where f is an arithmetical function. We show that this function has many properties like the Ramanujan sum. Firstly we study the
partial summation formula involving Sf(m,n) and taking f=, we obtain the Dirichlet series with the coefficients S(m,n) and S(m,n)d(m). Moreover we show a certain property which is analogous to the orthogonality relation of the Ramanujan sums.