{"schema":"vela.problem-packet.v0.1","problem":49,"statement":"Let $A=\\{a_1<\\cdots<a_t\\}\\subseteq \\{1,\\ldots,N\\}$ be such that $\\phi(a_1)<\\cdots<\\phi(a_t)$. The primes are such an example. Are they the largest possible? Can one show that $\\lvert A\\rvert<(1+o(1))\\pi(N)$ or even $\\lvert A\\rvert=o(N)$?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A365339","name":"Length of the longest subsequence of 1,...,n on which the Euler totient function phi A000010 is nondecreasing.","terms":"1,2,3,4,5,5,6,6,7,7,8,8,9,9,10,11,12,12,13,13,13,13,14,14,14,14,15,15,16,16,17,17,17,17,18,18,19,19,19,19,20,20,21,21,21","url":"https://oeis.org/A365339"},{"id":"A365474","name":"a(n) = A365339(10^n).","terms":"1,7,34,193,1276,9656,78562,664643,5761519,50847598","url":"https://oeis.org/A365474"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}