A049100 a(n) = Euler phi function applied 4 times to n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 2, 4, 1, 4, 2, 2, 2, 4, 2, 4, 2, 2, 4, 4, 2, 4, 4, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 4, 2, 4, 8, 2, 8, 2, 4, 4, 8, 2, 4, 4, 4, 4, 4, 4, 8, 2, 4, 4, 8, 4, 8, 4, 4

Offset

1,17

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

Formula

a(n) = phi(phi(phi(phi(n)))) = A000010(A000010(A000010(A000010(n)))) = A010554(A010554(n)) = A000010(A049099(n)).

Example

n=163, the successive iterates applying Euler totient function are as follows: 163,162,54,18,6,2,1. The 5th term is 6, when Phi was applied 4 times. So a(163)=6.

Maple

with(numtheory): seq(phi(phi(phi(phi(n)))), n=1..130); # Emeric Deutsch, May 14 2006

Mathematica

a(n)=Nest[ EulerPhi, n, 4 ]

Prog

(PARI) A049100(n) = eulerphi(eulerphi(eulerphi(eulerphi(n)))); \\ Antti Karttunen, Aug 22 2017

Crossrefs

Cf. A000010, A010554, A049099, A049107, A049115.

Sequence in context: A361691 A334933 A371451 * A276088 A030612 A378660

Adjacent sequences: A049097 A049098 A049099 * A049101 A049102 A049103

Keyword

nonn

Author

Labos Elemer

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 23 2007

Status

approved