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A011260 Number of primitive polynomials of degree n over GF(2).
(Formerly M0107 N0132)
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; graph; refs; listen; history; text; internal format)



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.

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).


David W. Wilson, Table of n, a(n) for n=1..400

Joerg Arndt, Matters Computational (The Fxtbook)

R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209.

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 arXiv:1505.02211 [cs.AR], 2015.

P. Koopman, Complete lists up to N=32

F. Ruskey, Primitive and Irreducible Polynomials [Broken link ?]

Eric Weisstein's World of Mathematics, Primitive Polynomial.


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


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


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




N. J. A. Sloane



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Last modified August 15 21:23 EDT 2022. Contains 356148 sequences. (Running on oeis4.)