Erdős problem 488 · problems.science

Let $A$ be a finite set and $B=\{ n \geq 1 : a\mid n\textrm{ for some }a\in A\}.$ Is it true that, for every $m>n\geq \max(A)$ , $\frac{\lvert B\cap [1,m]\rvert }{m}< 2\frac{\lvert B\cap [1,n]\rvert}{n}?$

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