Erdős Problem 708

### What is the conjecture

https://www.erdosproblems.com/708

Let $g(n)$ be minimal such that for any $A\subseteq [2,\infty)\cap \mathbb{N}$ with $\lvert A\rvert =n$ and any set $I$ of $\max(A)$ consecutive integers there exists some $B\subseteq I$ with $\lvert B\rvert=g(n)$ such that
$$\prod_{a\in A} a \mid \prod_{b\in B}b.$$
Is it true that
$$g(n) \leq (2+o(1))n?$$
Or perhaps even $g(n)\leq 2n$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else