{"schema":"vela.problem-packet.v0.1","problem":408,"statement":"Let $\\phi(n)$ be the Euler totient function and $\\phi_k(n)$ be the iterated $\\phi$ function, so that $\\phi_1(n)=\\phi(n)$ and $\\phi_k(n)=\\phi(\\phi_{k-1}(n))$. Let\\[f(n) = \\min \\{ k : \\phi_k(n)=1\\}.\\]Does $f(n)/\\log n$ have a distribution function? Is $f(n)/\\log n$ almost always constant? What can be said about the largest prime factor of $\\phi_k(n)$ when, say, $k=\\log\\log n$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A049108","name":"a(n) is the number of iterations of Euler phi function needed to reach 1 starting at n (n is counted).","terms":"1,2,3,3,4,3,4,4,4,4,5,4,5,4,5,5,6,4,5,5,5,5,6,5,6,5,5,5,6,5,6,6,6,6,6,5,6,5,6,6,7,5,6,6,6,6,7,6,6,6,7,6,7,5,7,6,6,6,7,6,","url":"https://oeis.org/A049108"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}