{"schema":"vela.problem-packet.v0.1","problem":693,"statement":"Let $k\\geq 2$ and $n$ be sufficiently large depending on $k$. Let $A=\\{a_1&#60;a_2&#60;\\cdots \\}$ be the set of those integers in $[n,n^k]$ which have a divisor in $(n,2n)$. Estimate\\[\\max_{i} a_{i+1}-a_i.\\]Is this $\\leq (\\log n)^{O(1)}$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A391118","name":"Let B_n = {b_1 < b_2 < ...} be the set of those integers in [n, n^2] which have a divisor in (n, 2n). a(n) = max(b_(i+1) - b_i).","terms":"3,3,3,3,4,4,4,4,5,6,6,5,6,6,6,6,6,6,8,8,8,8,8,7,8,8,8,8,8,8,8,8,8,8,8,8,8,7,9,9,10,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,1","url":"https://oeis.org/A391118"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}