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Number of iterations of phi(n) if n is a perfect totient number.
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%I #12 Apr 14 2023 03:48:15

%S 2,3,4,4,5,5,6,7,6,8,7,8,8,7,8,10,11,11,11,11,9,10,12,10,14,13,11,16,

%T 14,12,16,17,13,14,19,15,20,16,17,18,18,19,24,19,20,21,22,29,32,28,30,

%U 22,29,23,30,32,24,25,31,35,26,34,35,27

%N Number of iterations of phi(n) if n is a perfect totient number.

%C Let phi^{i} denote the i-th iteration of phi. a(n) is the smallest integer k such that phi^{k}(n) = 1 and Sum_{1<=i<=a(n)} phi^{i}(n) = n.

%H Paul Loomis, Michael Plytage and John Polhill, <a href="http://www.jstor.org/stable/27646564">Summing up the Euler phi function</a>, The College Mathematics Journal, Vol. 39, No. 1, Jan. 2008, pp. 34-42.

%H Peter Luschny, Sequences related to <a href="http://oeis.org/wiki/User:Peter_Luschny/EulerTotient">Euler's totient</a> function.

%F a(n) = A049108(A082897(n)) - 1. - _Amiram Eldar_, Apr 14 2023

%t lst = (* get list from A082897 *); f[n_] := Length@ FixedPointList[ EulerPhi@ # &, n] - 2; f@# & /@ lst (* _Robert G. Wilson v_, Nov 06 2010 *)

%Y Cf. A000010, A082897, A053478, A049108.

%K nonn,more

%O 1,1

%A _Peter Luschny_, Nov 02 2010

%E More terms from _Robert G. Wilson v_, Nov 06 2010

%E More terms from _Amiram Eldar_, Apr 14 2023