{"schema":"vela.problem-packet.v0.1","problem":1064,"statement":"Prove that $\\phi(n)&#62;\\phi(n-\\phi(n))$ for almost all $n$, but that $\\phi(n)&#60;\\phi(n-\\phi(n))$ for infinitely many $n$, where $\\phi$ is Euler's totient function.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A051487","name":"Numbers k such that phi(k) = phi(k - phi(k)).","terms":"2,6,12,24,48,96,150,192,300,384,600,726,750,768,1200,1452,1500,1536,2310,2400,2904,3000,3072,3174,3750,4620,4800,5046,58","url":"https://oeis.org/A051487"},{"id":"A051488","name":"Numbers k such that phi(k) < phi(k - phi(k)).","terms":"30,60,66,120,132,138,174,210,240,246,264,276,318,330,348,420,480,492,498,510,528,534,552,630,636,660,678,690,696,786,840","url":"https://oeis.org/A051488"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}