Series of Reciprocal Powers of k-almost Primes

2008/03/06 by Richard J. Mathar, Mathar, Richard J. · 1 citation
Mathematics · Physics and Astronomy · #11Y60 #33F05 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0803.0900

openalex publication_date 2008/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

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• Errata and Addenda to Mathematical Constants

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