A230919 Non-cyclic numbers n such that phi(n)^phi(n) == gcd(n, phi(n)) (mod n), where phi is Euler totient function.

12, 48, 56, 80, 192, 240, 252, 351, 448, 768, 992, 1100, 1134, 1260, 1280, 1824, 1872, 2016, 3072, 3300, 3520, 3584, 3840, 3875, 4352, 5103, 6156, 9072, 9120, 9288, 9477, 9984, 10962, 11132, 11264, 12288, 13056, 16128, 16256, 20480, 20592, 21760, 22736

Offset

1,1

Comments

The cyclic numbers satisfy phi(n)^phi(n) == gcd(n, phi(n))== 1 (mod n).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..3238

Mathematica

Select[Range[40000], PowerMod[EulerPhi[#], EulerPhi[#], #] > 1 && PowerMod[EulerPhi[#], EulerPhi[#], #] == GCD[#, EulerPhi[#]] &]

Prog

(PARI) is(n)=my(p=eulerphi(n), g=gcd(p, n)); g>1 && Mod(p, n)^p==g \\ Charles R Greathouse IV, Dec 27 2013

Crossrefs

Cf. A003277, A230918.

Sequence in context: A002612 A124351 A335101 * A181925 A118903 A324747

Adjacent sequences: A230916 A230917 A230918 * A230920 A230921 A230922

Keyword

nonn

Author

José María Grau Ribas, Nov 01 2013

Status

approved