A049107 a(n) = Euler phi function applied 5 times to n.

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

Offset

1,41

Links

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

Formula

a(n) = A000010(A049100(n)) = A010554(A049099(n)) = phi(phi(phi(phi(phi(n))))), where phi = A000010. - Antti Karttunen, Aug 22 2017

Example

For n = 163, the successive iterates applying Euler totient function are as follows: 163, 162, 54, 18, 6, 2, 1. The 6th term is 2, when Phi was applied 5 times. So a(163)=2, already a power of 2.
For n = 487, the successive iterates are 486, 162, 54, 18, 6, 2, 1. On the fifth iteration we reach 6, thus a(487) = 6. This is also the first term of A049107 that is not a power of 2. - Antti Karttunen, Aug 22 2017

Mathematica

a(n)=Nest[ EulerPhi, n, 5 ]
Nest[EulerPhi, Range[110], 5] (* Harvey P. Dale, May 19 2019 *)

Prog

(PARI) A049107(n) = eulerphi(eulerphi(eulerphi(eulerphi(eulerphi(n))))); \\ Antti Karttunen, Aug 22 2017

Crossrefs

Cf. A000010, A010554, A049099, A049100, A049115.

Sequence in context: A208576 A307897 A008651 * A380451 A046597 A107910

Adjacent sequences: A049104 A049105 A049106 * A049108 A049109 A049110

Keyword

nonn

Author

Labos Elemer

Status

approved