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 A333612 #10 Mar 29 2020 02:11:54
%S A333612 1,2,3,4,5,9,11,13,16,17,29,37,47,49,53,81,101,107,113,149,173,197,
%T A333612 257,389,401,509,529,531,557,593,677,701,747,773,829,963,977,1109,
%U A333612 1297,1493,1675,1733,1901,2417,2761,2837,3089,3313,3329,3413,3467,3677,3803,3989
%N A333612 Numbers at which the sum of the iterated infinitary totient function (A091732) attains a record.
%C A333612 Analogous to A181659 with the infinitary totient function A091732 instead of the Euler totient function phi (A000010).
%C A333612 The corresponding record values are 0, 1, 3, 6, 10, 14, 20, 21, 29, 45, ... (see the link for more values).
%H A333612 Amiram Eldar, <a href="/A333612/b333612.txt">Table of n, a(n) for n = 1..500</a>
%H A333612 Amiram Eldar, <a href="/A333612/a333612.txt">Table of n, a(n), A333611(a(n)) for n=1..500</a>
%t A333612 f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); s[n_] := Plus @@ NestWhileList[iphi, n, # != 1 &] - n; seq = {}; smax = -1; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq
%Y A333612 Cf. A091732, A181659, A330400, A331407, A333611.
%K A333612 nonn
%O A333612 1,2
%A A333612 _Amiram Eldar_, Mar 28 2020