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A011260
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Number of primitive polynomials of degree n over GF(2).
(Formerly M0107 N0132)
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17
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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
(list;
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OFFSET
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1,3
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REFERENCES
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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.
R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.
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., 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).
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LINKS
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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.
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MAPLE
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with(numtheory): phi(2^n-1)/n;
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MATHEMATICA
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Table[EulerPhi[(2^n - 1)]/n, {n, 1, 50}]
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PROG
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(PARI) a(n)=eulerphi(2^n-1)/n - Hauke Worpel (thebigh(AT)outgun.com), Jun 10 2008
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CROSSREFS
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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
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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