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Let $a_1,a_2,\dots,a_k$ be positive integers with$\gcd(a_1,a_2,\dots,a_k)=1$. Frobenius number is the largest positive integerthat is NOT representable in terms of $a_1,a_2,\dots,a_k$. When $k\ge 3$, thereis no explicit formula in general, but some formulae may exist for specialsequences $a_1,a_2,\dots,a_k$, including, those forming arithmetic progressionsand their modifications. In this paper, we give formulae for the power andweighted sum of nonrepresentable positive integers. As applications, we showexplicit expressions of these sums for $a_1,a_2,\dots,a_k$ forming arithmeticprogressions.

Sylvester power and weighted sums on the Frobenius set in arithmetic progression