{"schema":"vela.problem-packet.v0.1","problem":1107,"statement":"Let $r\\geq 2$. A number $n$ is $r$-powerful if for every prime $p$ which divides $n$ we have $p^r\\mid n$. Is every large integer the sum of at most $r+1$ many $r$-powerful numbers?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A056828","name":"Numbers that are not the sum of at most three powerful numbers (A001694).","terms":"7,15,23,87,111,119","url":"https://oeis.org/A056828"},{"id":"A392342","name":"Numbers that are not the sum of at most four cubefull numbers.","terms":"5,6,7,12,13,14,15,20,21,22,23,31,38,39,46,47,53,58,69,77,79,85,95,101,103,111,175,196,212,228,231,247,327,444,458,490,60","url":"https://oeis.org/A392342"},{"id":"A392343","name":"Numbers that are not the sum of at most five 4-full numbers.","terms":"6,7,8,9,10,11,12,13,14,15,21,22,23,24,25,26,27,28,29,30,31,37,38,39,40,41,42,43,44,45,46,47,52,53,54,55,56,57,58,59,60,6","url":"https://oeis.org/A392343"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}