A069925 a(n) = phi(2^n+1)/(2*n).

1, 1, 1, 2, 2, 4, 6, 16, 18, 40, 62, 160, 210, 448, 660, 2048, 2570, 5184, 9198, 24672, 32508, 76032, 121574, 344064, 405000, 1005888, 1569780, 4511520, 6066336, 12672000, 23091222, 67004160, 85342752, 200422656, 289531200, 892477440

Offset: 1

Author

Benoit Cloitre, Apr 25 2002

Keywords

• easy
• nonn

Comments

Number of primitive self-reciprocal polynomials of degree 2*n over GF(2). - Joerg Arndt, Jul 04 2012

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1090
• Joerg Arndt, Matters Computational (The Fxtbook), section 40.8 "Self-reciprocal polynomials", pp. 846-848.
• Helmut Meyn and Werner Götz, Self-reciprocal Polynomials Over Finite Fields, Séminaire Lotharingien de Combinatoire, B21d, pp. 82-90, 1989.

Crossrefs

Cf. A011260 (degree-n primitive polynomials).

Cf. A000048 (degree-2*n irreducible self-reciprocal polynomials).

Cf. A000010, A000051, A053285.

Programs

Mathematica

Table[EulerPhi[2^n+1]/(2n),{n,50}] (* Harvey P. Dale, Nov 15 2011 *)

PARI

a(n) = eulerphi(2^n+1)/(2*n); /* Joerg Arndt, Jul 04 2012 */

Formula

a(n) = phi(2^n+1)/(2*n).

a(n) = A053285(n)/(2*n). - Amiram Eldar, Jun 02 2022