{"schema":"vela.problem-packet.v0.1","problem":1217,"statement":"Let $A=\\{a_1<a_2<\\cdots\\}$ be an infinite sequence of positive integers with positive lower logarithmic density.Must there exist a sequence $n_1<\\cdots$ such that\\[a_{n_i}\\mid a_{n_{i+1}}\\]for all $i\\geq 1$ and\\[\\limsup_{x\\to \\infty}\\frac{1}{\\log\\log x}\\sum_{a_{n_i}<x}1 \\geq \\limsup_{x\\to \\infty} \\frac{1}{\\log\\log x}\\sum_{a_n<x}\\frac{1}{a_n\\log a_n}?\\]","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)"}