

A011260


Number of primitive polynomials of degree n over GF(2).
(Formerly M0107 N0132)


22



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
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OFFSET

1,3


REFERENCES

E. R. Berlekamp, Algebraic Coding Theory, McGrawHill, NY, 1968, p. 84.
T. L. Booth, An analytical representation of signals in sequential networks, pp. 3013240 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.
R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198209.
P. Fan and M. Darnell, Sequence Design for Communications Applications, Wiley, NY, 1996, Table 5.1, p. 118.
W. W. Peterson and E. J. Weldon, Jr., ErrorCorrecting Codes. MIT Press, Cambridge, MA, 2nd edition, 1972, p. 476.
M. P. Ristenblatt, PseudoRandom Binary Coded Waveforms, pp. 274314 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

David W. Wilson, Table of n, a(n) for n=1..400
Joerg Arndt, Matters Computational (The Fxtbook)
Karthik Ganesan, Alexander Hu, Subhasish Mitra, H.S. Philip Wong, Simon Wong, Tony F. Wu, TPAD: Hardware Trojan Prevention and Detection for Trusted Integrated Circuits, arXiv preprint, 2015.
P. Koopman, Complete lists up to N=32
F. Ruskey, Primitive and Irreducible Polynomials
Eric Weisstein's World of Mathematics, Primitive Polynomial.


MAPLE

with(numtheory): phi(2^n1)/n;


MATHEMATICA

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


PROG

(PARI) a(n)=eulerphi(2^n1)/n  Hauke Worpel (thebigh(AT)outgun.com), Jun 10 2008


CROSSREFS

See A058947 for initial terms. Cf. A001037, A000020.
Cf. A027695.
Sequence in context: A140833 A257389 A071908 * A117855 A086442 A071407
Adjacent sequences: A011257 A011258 A011259 * A011261 A011262 A011263


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


STATUS

approved



