English

A Formula For the Number of $k$-almost Primes

Number Theory 2023-10-24 v1

Abstract

In 2005, E. Noel and G. Panos constructed a formula to count the number of semiprimes less than a given value xx. In 2006, this formula was rediscovered independently by R.G. Wilson V. However, each citation of this result was simply through personal communication, and a formal proof has not been written down anywhere in the literature. In this article, we generalize their formula to the case of kk-almost primes and square-free kk-almost primes.

Keywords

Cite

@article{arxiv.2310.14989,
  title  = {A Formula For the Number of $k$-almost Primes},
  author = {Steven Creech},
  journal= {arXiv preprint arXiv:2310.14989},
  year   = {2023}
}