{"schema":"vela.problem-packet.v0.1","problem":444,"statement":"Let $A\\subseteq\\mathbb{N}$ be infinite and $d_A(n)$ count the number of $a\\in A$ which divide $n$. Is it true that, for every $k$,\\[\\limsup_{x\\to \\infty} \\frac{\\max_{n<x}d_A(n)}{\\left(\\sum_{n\\in A\\cap[1,x)}\\frac{1}{n}\\right)^k}=\\infty?\\]","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)"}