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A011260 Number of primitive polynomials of degree n over GF(2).
(Formerly M0107 N0132)
24

%I M0107 N0132

%S 1,1,2,2,6,6,18,16,48,60,176,144,630,756,1800,2048,7710,7776,27594,

%T 24000,84672,120032,356960,276480,1296000,1719900,4202496,4741632,

%U 18407808,17820000,69273666,67108864,211016256,336849900,929275200,725594112,3697909056

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

%D E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.

%D 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.

%D P. Fan and M. Darnell, Sequence Design for Communications Applications, Wiley, NY, 1996, Table 5.1, p. 118.

%D W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes. MIT Press, Cambridge, MA, 2nd edition, 1972, p. 476.

%D M. P. Ristenblatt, Pseudo-Random Binary Coded Waveforms, pp. 274-314 of R. S. Berkowitz, editor, Modern Radar, Wiley, NY, 1965; see p. 296.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David W. Wilson, <a href="/A011260/b011260.txt">Table of n, a(n) for n=1..400</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>

%H R. Church, <a href="http://www.jstor.org/stable/1968675">Tables of irreducible polynomials for the first four prime moduli</a>, Annals Math., 36 (1935), 198-209.

%H Karthik Ganesan, Alexander Hu, Subhasish Mitra, H.-S. Philip Wong, Simon Wong, Tony F. Wu, <a href="http://arxiv.org/abs/1505.02211">TPAD: Hardware Trojan Prevention and Detection for Trusted Integrated Circuits</a>, arXiv preprint arXiv:1505.02211 [cs.AR], 2015.

%H P. Koopman, <a href="http://users.ece.cmu.edu/~koopman/lfsr/index.html">Complete lists up to N=32</a>

%H F. Ruskey, <a href="http://www.theory.cs.uvic.ca/~cos/inf/neck/PolyInfo.html">Primitive and Irreducible Polynomials</a> [Broken link ?]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimitivePolynomial.html">Primitive Polynomial.</a>

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

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

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

%Y See A058947 for initial terms. Cf. A001037, A000020.

%Y Cf. A027695.

%K nonn,easy,nice

%O 1,3

%A _N. J. A. Sloane_.

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Last modified November 27 15:50 EST 2020. Contains 338683 sequences. (Running on oeis4.)