Multiplicative bases and an Erd\H{o}s problem
  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? 
P\'eter P\'al Pach, Csaba S\'andor
math.NT