OPEN
Let $\epsilon>0$. Is it true that, for all large $n$, the number of divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/2-\epsilon})$ is $O_\epsilon(1)$?
Erdős attributes this conjecture to Ruzsa. Erdős and Rosenfeld
[ErRo97] proved that there are infinitely many $n$ such that there are four divisors of $n$ in $(n^{1/2},n^{1/2}+n^{1/4})$.
See also [887].
