{"schema":"vela.problem-packet.v0.1","problem":433,"statement":"If $A\\subset \\mathbb{N}$ is a finite set then let $G(A)$ denote the greatest integer which is not expressible as a finite sum of elements from $A$ (with repetitions allowed). Let\\[g(k,n)=\\max G(A)\\]where the maximum is taken over all $A\\subseteq \\{1,\\ldots,n\\}$ of size $\\lvert A\\rvert=k$ which has no common divisor. Is it true that\\[g(k,n)\\sim \\frac{n^2}{k-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)"}