{"schema":"vela.problem-packet.v0.1","problem":460,"statement":"Let $a_0=0$ and $a_1=1$, and in general define $a_k$ to be the least integer $>a_{k-1}$ for which $(n-a_k,n-a_i)=1$ for all $0\\leq i<k$. Does\\[\\sum_{0<a_i< n}\\frac{1}{a_i}\\to \\infty\\]as $n\\to \\infty$? What about if we restrict the sum to those $i$ such that $n-a_j$ is divisible by some prime $\\leq a_j$, or the complement of such $i$?","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)"}