  Sums over inverse s-th powers of semiprimes and k-almost primes are
transformed into sums over products of powers of ordinary prime zeta functions.
Multinomial coefficients known from the cycle decomposition of permutation
groups play the role of expansion coefficients. Founded on a known convergence
acceleration for the ordinary prime zeta functions, the sums and first
derivatives are tabulated with high precision for indices k=2,...,6 and integer
powers s=2,...,8.
