{"schema":"vela.problem-packet.v0.1","problem":940,"statement":"Let $r\\geq 3$. A number $n$ is $r$-powerful if for every prime $p$ which divides $n$ we have $p^r\\mid n$.Are there infinitely many integers which are not the sum of at most $r$ many $r$-powerful numbers? Does the set of integers which are the sum of at most $r$ $r$-powerful numbers have density $0$?","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)"}