{"schema":"vela.problem-packet.v0.1","problem":650,"statement":"Let $f(m)$ be such that if $A\\subseteq \\{1,\\ldots,N\\}$ has $\\lvert A\\rvert=m$ then every interval in $[1,\\infty)$ of length $2N$ contains $\\geq f(m)$ many distinct integers $b_1,\\ldots,b_r$ where each $b_i$ is divisible by some $a_i\\in A$, where $a_1,\\ldots,a_r$ are distinct.Estimate $f(m)$. In particular is it true that $f(m)\\leq \\sqrt{m}$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A027434","name":"a(1) = 2; then defined by property that a(n) = smallest number >= a(n-1) such that successive runs have lengths 1,1,2,2,3,3,4,4.","terms":"2,3,4,4,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,10,11,11,11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14","url":"https://oeis.org/A027434"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}