Problem Statement
Is there an absolute constant $K$ such that, for every $C>0$, if $n$ is sufficiently large then $n$ has at most $K$ divisors in $(n^{1/2},n^{1/2}+C n^{1/4})$.
Categories:
Number Theory Divisors
Progress
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.Source: erdosproblems.com/887 | Last verified: January 19, 2026