{"schema":"vela.problem-packet.v0.1","problem":1099,"statement":"Let $1=d_1<\\cdots<d_{\\tau(n)}=n$ be the divisors of $n$, and for $\\alpha>1$ let\\[h_\\alpha(n) = \\sum_i \\left( \\frac{d_{i+1}}{d_i}-1\\right)^\\alpha.\\]Is it true that\\[\\liminf_{n\\to \\infty}h_\\alpha(n) \\ll_\\alpha 1?\\]","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)"}