Multiplicative bases and an Erdős problem (1602.06724v1)

Abstract: In this paper we investigate how small the density of a multiplicative basis of order $h$ can be in ${1,2,\dots,n}$ and in $\mathbb{Z}^+$. Furthermore, a related problem of Erd\H os is also studied: How dense can a set of integers be, if none of them divides the product of $h$ others?