Series of Reciprocal Powers of k-almost Primes
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2008
- DOI:
- 10.48550/arXiv.0803.0900
- arXiv:
- arXiv:0803.0900
- Bibcode:
- 2008arXiv0803.0900M
- Keywords:
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- Mathematics - Number Theory;
- 11Y60;
- 33F05
- E-Print:
- Added Section 1, Equations 4+5, Remark 2, Table 2, and Section 4.3