{"schema":"vela.problem-packet.v0.1","problem":441,"statement":"Let $N\\geq 1$. What is the size of the largest $A\\subset \\{1,\\ldots,N\\}$ such that $[a,b]\\leq N$ for all $a,b\\in A$, where $[a,b]$ is the least common multiple of $a$ and $b$?Is it attained by choosing all integers in $[1,(N/2)^{1/2}]$ together with all even integers in $[(N/2)^{1/2},(2N)^{1/2}]$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A068509","name":"a(n) = maximum length of a subset in {1,..,n} whose integers have pairwise LCM not exceeding n.","terms":"1,2,2,3,3,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10","url":"https://oeis.org/A068509"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}