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 A334814 #9 May 12 2020 13:00:04
%S A334814 1,2,3,5,11,29,107,257,941,2017,11261,45039,441073,2151073,8575873,
%T A334814 42884161,220268161,440536321
%N A334814 Least number that reaches 1 after n iterations of the map k -> sigma(k)/d(k) if d(k) | sigma(k), and k -> 1 otherwise, where d(k) is the number of divisors of k (A000005) and sigma(k) is their sum (A000203).
%C A334814 Apparently, most of the terms are primes. 45039 = 3 * 15013 is the first composite term.
%C A334814 a(18) > 2*10^10, if it exists.
%e A334814 a(3) = 5 since sigma(5)/d(5) = 6/2 = 3, sigma(3)/d(3) = 4/2 = 2, and sigma(2)/d(2) = 3/2 is not an integer, hence there are 3 iterations: 5 -> 3 -> 2 -> 1, and 5 is the least number with 3 iterations.
%t A334814 rat[n_] := If[IntegerQ[r = DivisorSigma[1, n]/DivisorSigma[0, n]], r, 1]; f[n_] := Length @ FixedPointList[rat, n] - 1; max = 10; seq = Table[0, {max}]; c = 0; n = 1; While[c < max, i = f[n]; If[i <= max && seq[[i]] == 0, c++; seq[[i]] = n]; n++]; seq
%Y A334814 Cf. A000005, A000203, A003601, A102187, A330816, A334813.
%K A334814 nonn,more
%O A334814 0,2
%A A334814 _Amiram Eldar_, May 12 2020