{"schema":"vela.problem-packet.v0.1","problem":393,"statement":"Let $f(n)$ denote the minimal $m\\geq 1$ such that\\[n! = a_1\\cdots a_t\\]with $a_1&#60;\\cdots &#60;a_t=a_1+m$. What is the behaviour of $f(n)$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A388302","name":"a(n) = is the smallest m >= 1 such that n! = b_1*...*b_t with b_1 < ... < b_t and m = b_t - b_1.","terms":"1,1,2,2,2,2,4,6,7,6,9,9,9,12,14,12,15,16,17,18,19,19,20,21,22,24,24,24,27,27,29,30,30,32,34,33,34,34,37,37,38,38,39,41,4","url":"https://oeis.org/A388302"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}