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

1,11

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.

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A366844 A002300 A350063 * A181776 A243036 A230224

Adjacent sequences: A049096 A049097 A049098 * A049100 A049101 A049102

Keyword

nonn

Author

Labos Elemer

Status

approved