{"schema":"vela.problem-packet.v0.1","problem":390,"statement":"Let $f(n)$ be the minimal $m$ such that\\[n! = a_1\\cdots a_k\\]with $n< a_1<\\cdots <a_k=m$. Is there (and what is it) a constant $c$ such that\\[f(n)-2n \\sim c\\frac{n}{\\log n}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A193429","name":"a(n) = minimum value of the largest element of a nonempty set of positive integers > n such that their product is equal to n!, or 0 if no such set exists.","terms":"1,0,0,6,24,12,10,20,16,28,25,22,33,30,28,28,39,35,36,44,44,42,44,50,50,50,57,57,56,58,65,64,64,72,72,70,75,80,80,78,80,8","url":"https://oeis.org/A193429"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}