{"schema":"vela.problem-packet.v0.1","problem":1000,"statement":"Let $A=\\{n_1<n_2<\\cdots\\}$ be an infinite sequence of integers, and let $\\phi_A(k)$ count the number of $1\\leq m\\leq n_k$ such that the fraction $\\frac{m}{n_k}$ does not have denominator $n_j$ for $j<k$ when written in lowest form; equivalently,\\[\\frac{n_k}{(m,n_k)}\\neq n_j\\]for all $1\\leq j<k$.Is there a sequence $A$ such that\\[\\lim_{N\\to \\infty}\\frac{1}{N}\\sum_{k\\leq N}\\frac{\\phi_A(k)}{n_k}=0?\\]","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)"}