Geodesic
$S$-exponential numbers
Vladimir Shevelev1
1 Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva 84105, Israel
Acta Arithmetica, Tome 175 (2016) no. 4, pp. 385-395

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We prove that, for every set $S$ of positive integers containing 1 (finite or infinite), the density $h(E(S))$ of the set $E(S)$ of numbers that have prime factorizations with exponents only from $S$ exists, and we give an explicit formula for it. Further, we study the set of such densities for all $S$ and prove that it is a perfect set with a countable set of gaps which are some left-sided neighborhoods of the densities corresponding to all finite $S$ except for $S=\{1\}.$
DOI : 10.4064/aa8395-5-2016
Keywords: prove every set positive integers containing finite infinite density set numbers have prime factorizations exponents only exists explicit formula further study set densities prove perfect set countable set gaps which left sided neighborhoods densities corresponding finite except

Vladimir Shevelev 1

1 Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva 84105, Israel 
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Vladimir Shevelev. $S$-exponential numbers. Acta Arithmetica, Tome 175 (2016) no. 4, pp. 385-395. doi: 10.4064/aa8395-5-2016

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