{"schema":"vela.problem-packet.v0.1","problem":269,"statement":"Let $P$ be a finite set of primes with $\\lvert P\\rvert \\geq 2$ and let $\\{a_1<a_2<\\cdots\\}=\\{ n\\in \\mathbb{N} : \\textrm{if }p\\mid n\\textrm{ then }p\\in P\\}$. Is the sum\\[\\sum_{n=1}^\\infty \\frac{1}{[a_1,\\ldots,a_n]},\\]where $[a_1,\\ldots,a_n]$ is the lowest common multiple of $a_1,\\ldots,a_n$, irrational?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}