{"schema":"vela.problem-packet.v0.1","problem":542,"statement":"Is it true that if $A\\subseteq\\{1,\\ldots,n\\}$ is a set such that $[a,b]>n$ for all $a\\neq b$, where $[a,b]$ is the least common multiple, then\\[\\sum_{a\\in A}\\frac{1}{a}\\leq \\frac{31}{30}?\\]Is it true that there must be $\\gg n$ many $m\\leq n$ which do not divide any $a\\in A$?","status":"solved","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)"}