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

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, 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, 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

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Paul Erdős, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204.
• Paul Erdos, Andrew Granville, Carl Pomerance and Claudia Spiro, On the normal behavior of the iterates of some arithmetic functions, Analytic number theory, Birkhäuser Boston, 1990, pp. 165-204. [Annotated copy with A-numbers]
• Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Crossrefs

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

Programs

Mathematica

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

PARI

A049099(n) = eulerphi(eulerphi(eulerphi(n))); \\ Antti Karttunen, Aug 22 2017

Formula

a(n) = A000010(A010554(n)) = A000010(A000010(A000010(n))). - Antti Karttunen, Aug 22 2017