Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set of all densities of exponentially S-numbers   Let $\mathbf{G}$ be the set of all finite or infinite increasing sequences of
positive integers beginning with 1. For a sequence $S=\{s(n)\}, n\geq1,$ 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.

20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ