A011260 Number of primitive polynomials of degree n over GF(2).

1, 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
• easy
• nice

References

• Elwyn 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.
• Pingzhi Fan and Michael Darnell, Sequence Design for Communications Applications, Wiley, NY, 1996, Table 5.1, p. 118.
• 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.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1206 (terms 1..400 from David W. Wilson)
• Joerg Arndt, Matters Computational (The Fxtbook).
• Randolph Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
• Philip Koopman, Complete lists up to N=32.
• Frank Ruskey, Primitive and Irreducible Polynomials [Wayback Machine link]
• Eric Weisstein's World of Mathematics, Primitive Polynomial.
• Tony F. Wu, Karthik Ganesan, Yunqing Alexander Hu, H.-S. Philip Wong, Simon Wong, and Subhasish Mitra, TPAD: Hardware Trojan Prevention and Detection for Trusted Integrated Circuits, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 35, No. 4 (2016), pp. 521-534; arXiv preprint, arXiv:1505.02211 [cs.AR], 2015.

Crossrefs

See A058947 for initial terms.

Cf. A000010, A000020, A001037, A027695.

Programs

Maple

with(numtheory): phi(2^n-1)/n;

Mathematica

Table[EulerPhi[(2^n - 1)]/n, {n, 1, 50}]

PARI

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