{"schema":"vela.problem-packet.v0.1","problem":220,"statement":"Let $n\\geq 1$ and\\[A=\\{a_1&#60;\\cdots &#60;a_{\\phi(n)}\\}=\\{ 1\\leq m&#60;n : (m,n)=1\\}.\\]Is it true that\\[ \\sum_{1\\leq k&#60;\\phi(n)}(a_{k+1}-a_k)^2 \\ll \\frac{n^2}{\\phi(n)}?\\]","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A322144","name":"a(n) = Sum_{i=1..phi(n)-1} (r(i+1)-r(i))^2 where r(1) = 1 < ... < n-1 = r(phi(n)) are the phi(n) integers relatively prime to n.","terms":"0,0,1,4,3,16,5,12,11,24,9,36,11,32,29,28,15,56,17,52,39,48,21,76,31,56,41,68,27,128,29,60,59,72,57,116,35,80,69,108,39,1","url":"https://oeis.org/A322144"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}