{"schema":"vela.problem-packet.v0.1","problem":291,"statement":"Let $n\\geq 1$ and define $L_n$ to be the least common multiple of $\\{1,\\ldots,n\\}$ and $a_n$ by\\[\\sum_{1\\leq k\\leq n}\\frac{1}{k}=\\frac{a_n}{L_n}.\\]Is it true that $(a_n,L_n)=1$ and $(a_n,L_n)>1$ both occur for infinitely many $n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A110566","name":"a(n) = lcm{1,2,...,n}/denominator of harmonic number H(n).","terms":"1,1,1,1,1,3,3,3,1,1,1,1,1,1,1,1,1,3,3,15,45,45,45,15,3,3,1,1,1,1,1,1,11,11,11,11,11,11,11,11,11,77,77,7,7,7,7,7,1,1,1,1,","url":"https://oeis.org/A110566"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}