Erdős Problem #539

declared status 'open'. Formalized: yes. Let $h(n)$ be such that, for any set $A\subseteq \mathbb{N}$ of size $n$, the set$$\left\{ \frac{a}{(a,b)}: a,b\in A\right\}$$has size at least $h(n)$. Estimate $h(n)$. Prize: no. Tags: number theory.

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