A000020 Number of primitive polynomials of degree n over GF(2) (version 2).

2, 1, 2, 2, 6, 6, 18, 16, 48, 60, 176, 144, 630, 756, 1800, 2048, 7710, 7776, 27594, 24000, 84672, 120032, 356960, 276480, 1296000, 1719900, 4202496, 4741632, 18407808, 17820000, 69273666, 67108864, 211016256, 336849900, 929275200, 725594112, 3697909056

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The initial 2 should really be a 1. See A011260 for official version.

References

• E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
• T. L. Booth, An analytical representation of signals in sequential networks, pp. 301-3240 of Proceedings of the Symposium on Mathematical Theory of Automata. New York, N.Y., 1962. Microwave Research Institute Symposia Series, Vol. XII; Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, N.Y. 1963 xix+640 pp. See p. 303.
• W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes. MIT Press, Cambridge, MA, 2nd edition, 1972, p. 476.
• M. P. Ristenblatt, Pseudo-Random Binary Coded Waveforms, pp. 274-314 of R. S. Berkowitz, editor, Modern Radar, Wiley, NY, 1965; see p. 296.

Links

• David W. Wilson, Table of n, a(n) for n = 1..400
• R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
• S. V. Duzhin and D. V. Pasechnik, Groups acting on necklaces and sandpile groups, 2014. See p. 92. - _N. J. A. Sloane_, Jun 30 2014

Crossrefs

Cf. A058947, A011260 (with initial term 1).

Programs

Mathematica

Table[If[n==1,2,EulerPhi[2^n-1]/n],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)

PARI

a(n)=if(n==1,2,eulerphi(2^n-1)/n) \\ Hauke Worpel (thebigh(AT)outgun.com), Jun 10 2008