Weighted Sylvester sums on the Frobenius set.

Let a and b be relatively prime positive integers. In this paper the weighted sum ∑nεNR(a,b) λn−1nm is given explicitly or in terms of the Apostol- Bernoulli numbers, where m is a nonnegative integer, and NR(a, b) denotes the set of positive integers nonrepresentable in terms of a and b. [ABSTRACT FROM AUTHOR]