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A049100
a(n) = Euler phi function applied 4 times to n.
7
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 23 2007
STATUS
approved