{"schema":"vela.problem-packet.v0.1","problem":955,"statement":"Let\\[s(n)=\\sigma(n)-n=\\sum_{\\substack{d\\mid n\\\\ d<n}}d\\]be the sum of proper divisors function.If $A\\subset \\mathbb{N}$ has density $0$ then $s^{-1}(A)$ must also have density $0$.","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)"}