Set of all densities of exponentially S-numbers

Abstract

Let $\mathbf{G}$ be the set of all finite or infinite increasing sequences of positive integers beginning with 1. For a sequence $S=\{s(n)\},n\ge 1,$ from $\mathbf{G},$ a positive number $N$ is called an exponentially $S$-number $(N\in E(S)),$ if all exponents in its prime power factorization are in $S.$ The author \cite{2} proved that, for every sequence $S\in \mathbf{G},$ the sequence of exponentially $S$-numbers has a density $h=h(E(S))\in [\frac{6}{{\pi }^2},1].$ In this paper we study the set $\{h(E(S)\}$ of all such densities.

Addition a remark

References in corpus (1)

• Exponentially $S$-numbers

Cited by in corpus (1)

• On natural densities of sets of some type integers