{"schema":"vela.problem-packet.v0.1","problem":400,"statement":"For any $k\\geq 2$ let $g_k(n)$ denote the maximum value of\\[(a_1+\\cdots+a_k)-n\\]where $a_1,\\ldots,a_k$ are integers such that $a_1!\\cdots a_k! \\mid n!$. Can one show that\\[\\sum_{n\\leq x}g_k(n) \\sim c_k x\\log x\\]for some constant $c_k$? Is it true that there is a constant $c_k$ such that for almost all $n<x$ we have\\[g_k(n)=c_k\\log x+o(\\log x)?\\]","status":"open","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)"}