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 A330273 Infinitary perfect totient numbers: numbers that equal to the sum of their iterated infinitary totient function (A091732). 4
 3, 10, 21, 44, 93, 118, 170, 320, 548, 3596, 3620, 4772, 5564, 18260, 33051, 256425, 403700, 1071129, 1790160, 2318180, 3968852, 4027375, 10001319, 11270012, 12048740, 13358121, 31741593, 46271673, 56149161, 4344134553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The infinitary version of A082897 (perfect totient numbers), in which the infinitary totient function iphi (A091732) replaces the Euler totient function (A000010). LINKS EXAMPLE 10 is an infinitary perfect totient number because iphi(10) + iphi(iphi(10)) + ... = 4 + 3 + 2 + 1 = 10. MATHEMATICA 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] CROSSREFS Cf. A082897, A091732, A286067. Sequence in context: A268348 A117495 A007687 * A335666 A192033 A295063 Adjacent sequences:  A330270 A330271 A330272 * A330274 A330275 A330276 KEYWORD nonn,more AUTHOR Amiram Eldar, Dec 13 2019 STATUS approved

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Last modified September 20 19:27 EDT 2021. Contains 347589 sequences. (Running on oeis4.)