{"schema":"vela.problem-packet.v0.1","problem":890,"statement":"If $\\omega_k(n)$ counts the number of distinct prime factors of $n$ which are $>k$, then is it true that, for every $k\\geq 1$,\\[\\liminf_{n\\to \\infty}\\sum_{0\\leq i<k}\\omega_k(n+i)\\leq k?\\]Is it true that\\[\\limsup_{n\\to \\infty}\\left(\\sum_{0\\leq i<k}\\omega(n+i)\\right) \\frac{\\log\\log n}{\\log n}=1,\\]where $\\omega$ counts the number of distinct prime factors without restriction?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}