cp's OEIS Frontend

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.

A330273 Infinitary perfect totient numbers: numbers that equal to the sum of their iterated infinitary totient function (A091732).

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%I A330273 #21 Dec 13 2019 19:45:51
%S A330273 3,10,21,44,93,118,170,320,548,3596,3620,4772,5564,18260,33051,256425,
%T A330273 403700,1071129,1790160,2318180,3968852,4027375,10001319,11270012,
%U A330273 12048740,13358121,31741593,46271673,56149161,4344134553
%N A330273 Infinitary perfect totient numbers: numbers that equal to the sum of their iterated infinitary totient function (A091732).
%C A330273 The infinitary version of A082897 (perfect totient numbers), in which the infinitary totient function iphi (A091732) replaces the Euler totient function (A000010).
%e A330273 10 is an infinitary perfect totient number because iphi(10) + iphi(iphi(10)) + ... = 4 + 3 + 2 + 1 = 10.
%t A330273 f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1); infPerfTotQ[n_] := Plus @@ FixedPointList[iphi@# &, n] == 2 n + 1; Select[Range[1000], infPerfTotQ]
%Y A330273 Cf. A082897, A091732, A286067.
%K A330273 nonn,more
%O A330273 1,1
%A A330273 _Amiram Eldar_, Dec 13 2019