{"schema":"vela.problem-packet.v0.1","problem":1106,"statement":"Let $p(n)$ denote the partition function of $n$ and let $F(n)$ count the number of distinct prime factors of\\[\\prod_{1\\leq k\\leq n}p(k).\\]Does $F(n)\\to \\infty$ with $n$? Is $F(n)>n$ for all sufficiently large $n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A194259","name":"Number of distinct prime factors of p(1)*p(2)*...*p(n), where p(n) is the n-th partition number.","terms":"0,1,2,3,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,8,9,9,10,11,12,13,14,15,16,17,17,18,19,20,21,21,21,22,23,24,25,27,28,30,31,32,","url":"https://oeis.org/A194259"},{"id":"A194260","name":"A194259(n) - n, where A194259(n) is the number of distinct prime factors of p(1)*p(2)*...*p(n) and p(n) is the n-th partition number.","terms":"-1,-1,-1,-1,-1,-1,-2,-3,-4,-5,-6,-7,-7,-8,-9,-10,-11,-12,-13,-13,-14,-14,-14,-15,-15,-15,-15,-15,-15,-15,-15,-15,-16,-16","url":"https://oeis.org/A194260"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}