Problem 942

Erdős Problem #942: declared status 'open'. Formalized: yes. Let $h(n)$ count the number of powerful (if $p\mid m$ then $p^2\mid m$) integers in $[n^2,(n+1)^2)$. Estimate $h(n)$. In particular is there some constant $c>0$ such that$$h(n) < (\log n)^{c+o(1)}$$and, for infinitely many $n$,$$h(n) >(\log n)^{c-o(1)}?$$ Prize: no. Tags: number theory.