{"schema":"vela.problem-packet.v0.1","problem":131,"statement":"Let $F(N)$ be the maximal size of $A\\subseteq\\{1,\\ldots,N\\}$ such that no $a\\in A$ divides the sum of any distinct elements of $A\\backslash\\{a\\}$. Estimate $F(N)$. In particular, is it true that\\[F(N) > N^{1/2-o(1)}?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A068063","name":"Maximum cardinality of a nondividing subset of {1, 2, ..., n}.","terms":"0,1,1,2,2,2,2,3,3,3,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,","url":"https://oeis.org/A068063"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}