{"schema":"vela.problem-packet.v0.1","problem":685,"statement":"Let $\\epsilon>0$ and $n$ be large depending on $\\epsilon$. Is it true that for all $n^\\epsilon<k\\leq n^{1-\\epsilon}$ the number of distinct prime divisors of $\\binom{n}{k}$ is\\[(1+o(1))k\\sum_{k<p<n}\\frac{1}{p}?\\]Or perhaps even when $k \\geq (\\log n)^c$?","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)"}