%I #11 Mar 05 2020 03:43:42
%S 3,4,7,23,121,2857,5699,6377,9179,46537,63209,244967,654497,1067873,
%T 1112009,3435929,3831257,6441593,7589737,7784507,8149751,14307856,
%U 22434089,24007727,24571871,44503417,44926463,56732729,128199059,140830367,190145936,401767631,403152737
%N Infinitary phibonacci numbers: solutions k of the equation iphi(k) = iphi(k-1) + iphi(k-2) where iphi(k) is an infinitary analog of Euler's phi function (A091732).
%H Amiram Eldar, <a href="/A332971/b332971.txt">Table of n, a(n) for n = 1..70</a>
%e 7 is a term since iphi(7) = 6 and iphi(5) + iphi(6) = 4 + 2 = 6.
%t f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten @ (f @@@ FactorInteger[n]) - 1); Select[Range[3, 10^5], iphi[#] == iphi[# - 1] + iphi[# - 2] &]
%Y An infinitary version of A065557.
%Y Cf. A065900, A075565, A076136, A076251, A091732, A145469, A291126, A291176, A292033, A294995.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 04 2020