{"schema":"vela.problem-packet.v0.1","problem":394,"statement":"Let $t_k(n)$ denote the least $m$ such that\\[n\\mid m(m+1)(m+2)\\cdots (m+k-1).\\]Is it true that\\[\\sum_{n\\leq x}t_2(n)\\ll \\frac{x^2}{(\\log x)^c}\\]for some $c>0$?Is it true that, for $k\\geq 2$,\\[\\sum_{n\\leq x}t_{k+1}(n) =o\\left(\\sum_{n\\leq x}t_k(n)\\right)?\\]","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A344005","name":"a(n) = smallest positive m such that n divides the oblong number m*(m+1).","terms":"1,1,2,3,4,2,6,7,8,4,10,3,12,6,5,15,16,8,18,4,6,10,22,8,24,12,26,7,28,5,30,31,11,16,14,8,36,18,12,15,40,6,42,11,9,22,46,1","url":"https://oeis.org/A344005"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}