A027695 Number of primitive polynomials of degree n over GF(4).

1, 2, 4, 12, 32, 120, 288, 1512, 4096, 15552, 48000, 240064, 552960, 3439800, 9483264, 35640000, 134217728, 673699800, 1451188224, 9644765256, 23685120000, 115605729792, 401556013056, 1996264531840, 4566087106560, 26244000000000, 89961392102400, 356237685227520

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1122 (terms 0..150 from Andrew Howroyd)

Crossrefs

Column k=4 of A369291.

Cf. A027742, A295501.

Programs

Maple

with(numtheory): seq(`if`(n=0, 1, phi(4^n-1)/n), n=0..27);

Mathematica

Join[{1}, Array[EulerPhi[4^# - 1]/# &, 30]] (* Paolo Xausa, Jun 17 2024 *)

PARI

a(n) = if(n==0, 1, eulerphi(4^n-1)/n) \\ Andrew Howroyd, Feb 01 2024

Formula

a(n) = A295501(n)/n = 2*A027742(n) for n >= 1. - Amiram Eldar, Nov 30 2024

Extensions

a(24) onwards from Andrew Howroyd, Feb 01 2024