{"schema":"vela.problem-packet.v0.1","problem":784,"statement":"Let $C>0$. Does there exist a $c>0$ (depending on $C$) such that, for all sufficiently large $x$, if $A\\subseteq [1,x]$ has $\\sum_{n\\in A}\\frac{1}{n}\\leq C$ then\\[\\#\\{ m\\leq x : a\\nmid m\\textrm{ for all }a\\in A\\}\\gg\\frac{x}{(\\log x)^c}?\\]","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)"}