{"schema":"vela.problem-packet.v0.1","problem":401,"statement":"Is there some function $f(r)$ such that $f(r)\\to \\infty$ as $r\\to\\infty$, such that, for infinitely many $n$, there exist $a_1,a_2$ with\\[a_1+a_2> n+f(r)\\log n\\]such that $a_1!a_2! \\mid n!2^n3^n\\cdots p_r^n$?","status":"solved","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)"}