{"schema":"vela.problem-packet.v0.1","problem":534,"statement":"What is the largest possible subset $A\\subseteq\\{1,\\ldots,N\\}$ which contains $N$ such that $\\mathrm{gcd}(a,b)>1$ for all $a\\neq b\\in A$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A387543","name":"a(n) is the size of the largest subset of {1, 2, ..., n} containing n in which any two numbers share a prime factor.","terms":"1,1,1,2,1,3,1,4,3,5,1,6,1,7,5,8,1,9,1,10,7,11,1,12,5,13,9,14,1,15,1,16,11,17,7,18,1,19,13,20,1,21,1,22,15,23,1,24,7,25,1","url":"https://oeis.org/A387543"},{"id":"A387698","name":"Irregular triangle read by rows in which row n is the maximum clique containing n in the gcd-graph of {1, 2, ..., n}. If more than one such clique exists, choose the lexicographically earliest.","terms":"1,2,3,2,4,5,2,4,6,7,2,4,6,8,3,6,9,2,4,6,8,10,11,2,4,6,8,10,12,13,2,4,6,8,10,12,14,3,6,9,12,15,2,4,6,8,10,12,14,16,17,2,4","url":"https://oeis.org/A387698"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}