OPEN
Is there an absolute constant $K$ such that, for every $\epsilon>0$, if $n$ is sufficiently large then $n$ has at most $K$ divisors in $(n^{1/2},n^{1/2}+\epsilon n^{1/4})$.
A question of Erdős and Rosenfeld
[ErRo97], who proved that there are infinitely many $n$ with $4$ divisors in $(n^{1/2},n^{1/2}+n^{1/4})$, and ask whether $4$ is best possible here.
