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A049099 a(n) = Euler phi function applied thrice to n. 7

%I #24 Nov 29 2023 06:58:06

%S 1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,2,4,1,2,2,2,2,4,2,4,2,2,2,4,2,4,4,4,4,

%T 4,2,4,2,4,4,8,2,4,4,4,4,10,4,4,4,8,4,8,2,8,4,4,4,12,4,8,4,4,8,8,4,8,

%U 8,8,4,8,4,8,4,8,4,8,4,8,8,6,8,16,4,16,4,8,8,16,4,8,8,8,10,8,8,16,4,8,8,16

%N a(n) = Euler phi function applied thrice to n.

%H Antti Karttunen, <a href="/A049099/b049099.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="http://math.dartmouth.edu/~carlp/iterate.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.

%H Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, <a href="/A000010/a000010_1.pdf">On the normal behavior of the iterates of some arithmetic functions</a>, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [Of] Integer Sequences And Pairing Functions</a>, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

%F a(n) = A000010(A010554(n)) = A000010(A000010(A000010(n))). - _Antti Karttunen_, Aug 22 2017

%e n=163: the successive iterates of Euler totient function are 163,162,54,18,6,2,1. The 4th term is 18, when Phi was applied 3 times. So a(163)=18.

%t a(n)=Nest[ EulerPhi, n, 3 ]

%o (PARI) A049099(n) = eulerphi(eulerphi(eulerphi(n))); \\ _Antti Karttunen_, Aug 22 2017

%Y Cf. A000010, A010554, A049100, A049107, A049115.

%K nonn

%O 1,11

%A _Labos Elemer_

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)