{"schema":"vela.problem-packet.v0.1","problem":392,"statement":"Let $A(n)$ denote the least value of $t$ such that\\[n!=a_1\\cdots a_t\\]with $a_1\\leq \\cdots \\leq a_t\\leq n^2$. Is it true that\\[A(n)=\\frac{n}{2}-\\frac{n}{2\\log n}+o\\left(\\frac{n}{\\log n}\\right)?\\]","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)"}