Erdős Problem 711

### What is the conjecture

https://www.erdosproblems.com/711

Let $f(n,m)$ be minimal such that in $(m,m+f(n,m))$ there exist distinct integers $a_1,\ldots,a_n$ such that $k\mid a_k$ for all $1\leq k\leq n$. Prove that
$$\max_m f(n,m) \leq n^{1+o(1)}$$
and that
$$\max_m (f(n,m)-f(n,n))\to \infty.$$

Status: open