{"schema":"vela.problem-packet.v0.1","problem":942,"statement":"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 $c&#62;0$ such that\\[h(n) < (\\log n)^{c+o(1)}\\]and, for infinitely many $n$,\\[h(n) >(\\log n)^{c-o(1)}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}