{"schema":"vela.problem-packet.v0.1","problem":796,"statement":"Let $k\\geq 2$ and let $g_k(n)$ be the largest possible size of $A\\subseteq \\{1,\\ldots,n\\}$ such that every $m$ has $<k$ solutions to $m=a_1a_2$ with $a_1<a_2\\in A$.Is it true that\\[g_3(n)=\\frac{\\log\\log n}{\\log n}n+(c+o(1))\\frac{n}{\\log n}\\]for some constant $c$?","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)"}