Power Sums Related to Semigroups ${\sl S}(d_1,d_2,d_3)$
  The explicit formulas for the sums of positive powers of the integers $s_i$ unrepresentable by the triple of integers $d_1,d_2,d_3\in {\mathbb N}, \gcd(d_1,d_2,d_3)=1$, are derived. 
Leonid G. Fel and Boris Y. Rubinstein