{"schema":"vela.problem-packet.v0.1","problem":413,"statement":"Let $\\omega(n)$ count the number of distinct primes dividing $n$. Are there infinitely many $n$ such that, for all $m<n$, we have $m+\\omega(m) \\leq n$?Can one show that there exists an $\\epsilon>0$ such that there are infinitely many $n$ where $m+\\epsilon \\omega(m)\\leq n$ for all $m&#60;n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A005236","name":"Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n.","terms":"2,3,4,5,6,8,9,10,12,14,17,18,20,24,26,28,30,33,38,42,48,50,54,60,65,74,82,84,90,98,102,108,110,114,126,129,138,150,164,1","url":"https://oeis.org/A005236"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}