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 A333870 #10 Apr 09 2020 05:23:48 %S A333870 0,1,2,1,2,2,3,1,2,2,3,2,3,3,2,1,2,2,3,2,3,3,4,2,2,3,2,3,4,2,3,1,3,2, %T A333870 3,2,3,3,3,2,3,3,4,3,2,4,5,2,3,2,2,3,4,2,3,3,3,4,5,2,3,3,3,1,3,3,4,2, %U A333870 4,3,4,2,3,3,2,3,3,3,4,2,2,3,4,3,2,4,4 %N A333870 The number of iterations of the absolute Möbius divisor function (A173557) required to reach from n to 1. %C A333870 Apparently, the least number that reaches 1 after k iterations is A082449(k-1) (checked numerically for 1 <= k <= 17). %H A333870 Amiram Eldar, <a href="/A333870/b333870.txt">Table of n, a(n) for n = 1..10000</a> %H A333870 Daeyeoul Kim, Umit Sarp, and Sebahattin Ikikardes, <a href="https://doi.org/10.3390/math7111083">Iterating the Sum of Möbius Divisor Function and Euler Totient Function</a>, Mathematics, Vol. 7, No. 11 (2019), pp. 1083-1094. %e A333870 a(3) = 2 since there are 2 iterations from 3 to 1: A173557(3) = 2 and A173557(2) = 1. %t A333870 f[p_, e_] := p - 1; u[1] = 1; u[n_] := Times @@ (f @@@ FactorInteger[n]);a[n_] := Length @ FixedPointList[u, n] - 2; Array[a, 100] %Y A333870 Cf. A003434, A082449, A173557. %K A333870 nonn %O A333870 1,3 %A A333870 _Amiram Eldar_, Apr 08 2020