{"schema":"vela.problem-packet.v0.1","problem":412,"statement":"Let $\\sigma_1(n)=\\sigma(n)$, the sum of divisors function, and $\\sigma_k(n)=\\sigma(\\sigma_{k-1}(n))$. Is it true that, for every $m,n\\geq 2$, there exist some $i,j$ such that $\\sigma_i(m)=\\sigma_j(n)$?","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A007497","name":"a(1) = 2, a(n) = sigma(a(n-1)).","terms":"2,3,4,7,8,15,24,60,168,480,1512,4800,15748,28672,65528,122880,393192,1098240,4124736,15605760,50328576,149873152,3712262","url":"https://oeis.org/A007497"},{"id":"A051572","name":"a(1) = 5, a(n) = sigma(a(n-1)).","terms":"5,6,12,28,56,120,360,1170,3276,10192,24738,61440,196584,491520,1572840,5433480,20180160,94859856,355532800,1040179456,21","url":"https://oeis.org/A051572"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}