A fast computation of density of exponentially $S$-numbers

Vladimir Shevelev

A fast computation of density of exponentially $S$-numbers

Number Theory 2016-02-16 v1

Authors: Vladimir Shevelev

Abstract

The author \cite{4} proved that, for every set $S$ of positive integers containing 1 (finite or infinite) there exists the density $h=h(E(S))$ of the set $E(S)$ of numbers whose prime factorizations contain exponents only from $S,$ and gave an explicit formula for $h(E(S)).$ In this paper we give an equivalent polynomial formula for $\log h(E(S))$ which allows to get a fast calculation of $h(E(S)).$

Keywords

exponentially $S$-numbers set density prime factorization explicit formula polynomial formula fast calculation number theory

Cite

@article{arxiv.1602.04244,
  title  = {A fast computation of density of exponentially $S$-numbers},
  author = {Vladimir Shevelev},
  journal= {arXiv preprint arXiv:1602.04244},
  year   = {2016}
}

Comments

7 pages

A fast computation of density of exponentially $S$-numbers

Abstract

Keywords

Cite

Comments

Related papers