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 A348264 #14 Jul 19 2022 22:32:33 %S A348264 0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1, %T A348264 0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0, %U A348264 0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,2,0,1,0 %N A348264 a(n) is the number of iterations that n requires to reach a fixed point under the map x -> A348173(x). %C A348264 a(n) first differs from A011765(n+2) at n = 84. %C A348264 The fixed points are terms of A348004, so a(n) = 0 if and only if n is a term of A348004. %C A348264 Conjecture: essentially partial sums of A219977 (verified for n <= 5000). %H A348264 Amiram Eldar, <a href="/A348264/b348264.txt">Table of n, a(n) for n = 1..10000</a> %e A348264 a(1) = 0 since 1 is in A348004. %e A348264 a(2) = 1 since there is one iteration of the map x -> A348173(x) starting from 2: 2 -> 1. %e A348264 a(84) = 2 since there are 2 iterations of the map x -> A348173(x) starting from 84: 84 -> 78 -> 39. %t A348264 f[p_, e_] := p^e - 1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := Plus @@ DeleteDuplicates[uphi /@ Select[Divisors[n], CoprimeQ[#, n/#] &]]; a[n_] := -2 + Length@ FixedPointList[s, n]; Array[a, 100] %Y A348264 Cf. A047994, A011765, A348004, A348173. %K A348264 nonn %O A348264 1,84 %A A348264 _Amiram Eldar_, Oct 09 2021