{"schema":"vela.problem-packet.v0.1","problem":381,"statement":"A number $n$ is highly composite if $\\tau(m)<\\tau(n)$ for all $m<n$, where $\\tau(m)$ counts the number of divisors of $m$. Let $Q(x)$ count the number of highly composite numbers in $[1,x]$.Is it true that\\[Q(x)\\gg_k (\\log x)^k\\]for every $k\\geq 1$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A002182","name":"Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.","terms":"1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,10080,15120,20160,25200,27720,45360,50400,55440,","url":"https://oeis.org/A002182"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}