{"schema":"vela.problem-packet.v0.1","problem":1109,"statement":"Let $f(N)$ be the size of the largest subset $A\\subseteq \\{1,\\ldots,N\\}$ such that every $n\\in A+A$ is squarefree. Estimate $f(N)$. In particular, is it true that $f(N)\\leq N^{o(1)}$, or even $f(N) \\leq (\\log N)^{O(1)}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A392164","name":"a(n) is the size of the largest subset S of {1,...,N} such that every element of S+S is squarefree.","terms":"1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,","url":"https://oeis.org/A392164"},{"id":"A392165","name":"Indices of record values in A392164.","terms":"1,5,19,23,37,41,59,87,101,105,113,131,151,159,167,195,203,239,259,303,307,403,451,499,517,553,573,609,645,701,719,787,80","url":"https://oeis.org/A392165"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}