{"schema":"vela.problem-packet.v0.1","problem":1062,"statement":"Let $f(n)$ be the size of the largest subset $A\\subseteq \\{1,\\ldots,n\\}$ such that there are no three distinct elements $a,b,c\\in A$ such that $a\\mid b$ and $a\\mid c$. How large can $f(n)$ be? Is $\\lim f(n)/n$ irrational?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_3da5e7afe39059f8","kind":"dead_end","claim":"attempted via frontier '?' (transfer_strength=n/a) -> no_progress","grade":"honest_null","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A038372","name":"Largest subset of integers [ 1...n ] such that no member divides two others.","terms":"1,2,2,3,4,4,5,6,6,7,8,8,9,10,10,11,12,12,13,14,14,15,16,16,17,18,19,20,21,21,22,22,22,23,24,24,25,26,26,27,28,28,29,30","url":"https://oeis.org/A038372"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}