{"schema":"vela.problem-packet.v0.1","problem":425,"statement":"Let $F(n)$ be the maximum possible size of a subset $A\\subseteq\\{1,\\ldots,N\\}$ such that the products $ab$ are distinct for all $a<b$. Is there a constant $c$ such that\\[F(n)=\\pi(n)+(c+o(1))n^{3/4}(\\log n)^{-3/2}?\\]If $A\\subseteq \\{1,\\ldots,n\\}$ is such that all products $a_1\\cdots a_r$ are distinct for $a_1<\\cdots <a_r$ then is it true that\\[\\lvert A\\rvert \\leq \\pi(n)+O(n^{\\frac{r+1}{2r}})?\\]","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)"}