{"schema":"vela.problem-packet.v0.1","problem":258,"statement":"Let $a_1,a_2,\\ldots$ be a sequence of positive integers with $a_n\\to \\infty$. Is\\[\\sum_{n} \\frac{\\tau(n)}{a_1\\cdots a_n}\\]irrational, where $\\tau(n)$ is the number of divisors of $n$?","status":"solved","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)"}