{"schema":"vela.problem-packet.v0.1","problem":938,"statement":"Let $A=\\{n_1<n_2<\\cdots\\}$ be the sequence of powerful numbers (if $p\\mid n$ then $p^2\\mid n$).Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A001694","name":"Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers).","terms":"1,4,8,9,16,25,27,32,36,49,64,72,81,100,108,121,125,128,144,169,196,200,216,225,243,256,288,289,324,343,361,392,400,432,4","url":"https://oeis.org/A001694"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}