This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A055020 #13 Mar 18 2024 03:30:08
%S A055020 2,2,2,2,1,2,2,3,2,2,1,3,2,2,2,2,1,2,1,2,2,2,1,3,2,2,1,2,1,2,2,2,2,2,
%T A055020 1,3,2,2,1,2,1,3,2,2,2,2,1,3,2,2,2,2,1,2,1,2,2,2,1,3,2,2,2,2,1,3,2,2,
%U A055020 1,2,1,3,2,2,2,2,1,2,1,4,2,2,1,2,2,2,1,2,1,2,2,2,2,2,1,3,2,2,1,2,1,2,1
%N A055020 Number of iterations of sigma() required until 2n (or greater) is reached.
%H A055020 Amiram Eldar, <a href="/A055020/b055020.txt">Table of n, a(n) for n = 2..10001</a>
%e A055020 sigma(sigma(sigma(9))) = 24 >= 2*9, so a(9) = 3.
%t A055020 a[n_] := -1 + Length@ NestWhileList[DivisorSigma[1, #] &, n, # < 2*n &]; Array[a, 100, 2] (* _Amiram Eldar_, Mar 18 2024 *)
%o A055020 (PARI) a(n) = {my(m = n, nn = 2*n, c = 0); while(m < nn, m = sigma(m); c++); c;} \\ _Amiram Eldar_, Mar 18 2024
%Y A055020 Cf. A000203, A055021.
%K A055020 nonn
%O A055020 2,1
%A A055020 _Jud McCranie_, May 31 2000