{"schema":"vela.problem-packet.v0.1","problem":440,"statement":"Let $A=\\{a_1<a_2<\\cdots\\}\\subseteq \\mathbb{N}$ be infinite and let $A(x)$ count the number of indices for which $\\mathrm{lcm}(a_i,a_{i+1})\\leq x$. Is it true that $A(x) \\ll x^{1/2}$? How large can\\[\\liminf \\frac{A(x)}{x^{1/2}}\\]be?","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)"}