English

The combinatorial method to compute the sum of the powers of primes

Number Theory 2021-12-01 v1

Abstract

We will generalize the combinatorial algorithms for computing π(x)\pi(x) to compute sums F(x)=pxpk{F(x) = \sum_{p \leq x} p^k} for kZ0k \in \mathbb{Z}_{\geq 0}. The detailed exposition of algorithms is included along with implementation details.

Keywords

Cite

@article{arxiv.2111.15545,
  title  = {The combinatorial method to compute the sum of the powers of primes},
  author = {Alexey Orlov},
  journal= {arXiv preprint arXiv:2111.15545},
  year   = {2021}
}