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 A385746 #4 Jul 11 2025 01:27:40
%S A385746 3,10,18,21,48,160,288,3252,9304,13965,68526,719631,1531101,1954782,
%T A385746 28900572,39189195,14708055957
%N A385746 Numbers that are equal to the sum of their iterated infinitary analog of the totient function A384247.
%C A385746 Numbers k such that A385745(k) = k.
%e A385746 n | a(n) | iterations | sum
%e A385746 --+------+-----------------------------------+----------------------------
%e A385746 1 | 3 | 3 -> 2 -> 1 | 2 + 1 = 3
%e A385746 2 | 10 | 10 -> 4 -> 3 -> 2 -> 1 | 4 + 3 + 2 + 1 = 10
%e A385746 3 | 18 | 18 -> 8 -> 4 -> 3 -> 2 -> 1 | 8 + 4 + 3 + 2 + 1 = 18
%e A385746 4 | 21 | 21 -> 12 -> 6 -> 2 -> 1 | 12 + 6 + 2 + 1 = 21
%e A385746 5 | 48 | 48 -> 30 -> 8 -> 4 -> 3 -> 2 -> 1 | 30 + 8 + 4 + 3 + 2 + 1 = 48
%t A385746 f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n];
%t A385746 infPerfTotQ[n_] := Plus @@ FixedPointList[iphi, n] == 2*n + 1; infPerfTotQ[1] = False; Select[Range[10^5], infPerfTotQ]
%o A385746 (PARI) iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2)))); }
%o A385746 s(n) = if(n == 1, 0, my(i = iphi(n)); i + s(i));
%o A385746 isok(k) = s(k) == k;
%Y A385746 Cf. A384247, A385744, A385745, A385747.
%Y A385746 Similar sequences: A082897, A286067, A330273.
%K A385746 nonn,more
%O A385746 1,1
%A A385746 _Amiram Eldar_, Jul 08 2025