Power sums related to semigroups \(S(d_1,d_2,d_3)\). (Q877757)

Let \(d_1,d_2,d_3\in\mathbb{N}\), \(\gcd(d_1,d_2,d_3)=1\). The authors establish explicit formulas for the sums of positive powers of the integers \(s_i\) which are unrepresentable as \(s=x_1d_1+x_2d_2+x_3d_3\). The proof is based on explicit calculations with generating functions.