cp's OEIS Frontend

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

%I A011260 M0107 N0132 #42 Feb 16 2025 08:32:32
%S A011260 1,1,2,2,6,6,18,16,48,60,176,144,630,756,1800,2048,7710,7776,27594,
%T A011260 24000,84672,120032,356960,276480,1296000,1719900,4202496,4741632,
%U A011260 18407808,17820000,69273666,67108864,211016256,336849900,929275200,725594112,3697909056
%N A011260 Number of primitive polynomials of degree n over GF(2).
%D A011260 Elwyn R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, NY, 1968, p. 84.
%D A011260 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 A011260 Pingzhi Fan and Michael Darnell, Sequence Design for Communications Applications, Wiley, NY, 1996, Table 5.1, p. 118.
%D A011260 W. W. Peterson and E. J. Weldon, Jr., Error-Correcting Codes. MIT Press, Cambridge, MA, 2nd edition, 1972, p. 476.
%D A011260 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 A011260 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A011260 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A011260 Amiram Eldar, <a href="/A011260/b011260.txt">Table of n, a(n) for n = 1..1206</a> (terms 1..400 from David W. Wilson)
%H A011260 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>.
%H A011260 Randolph 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 A011260 Philip Koopman, <a href="http://users.ece.cmu.edu/~koopman/lfsr/index.html">Complete lists up to N=32</a>.
%H A011260 Frank Ruskey, <a href="https://web.archive.org/web/20130923045922/http://www.theory.cs.uvic.ca/~cos/inf/neck/PolyInfo.html">Primitive and Irreducible Polynomials</a> [Wayback Machine link]
%H A011260 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimitivePolynomial.html">Primitive Polynomial</a>.
%H A011260 Tony F. Wu, Karthik Ganesan, Yunqing Alexander Hu, H.-S. Philip Wong, Simon Wong, and Subhasish Mitra, <a href="https://doi.org/10.1109/TCAD.2015.2474373">TPAD: Hardware Trojan Prevention and Detection for Trusted Integrated Circuits</a>, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 35, No. 4 (2016), pp. 521-534; <a href="https://arxiv.org/abs/1505.02211">arXiv preprint</a>, arXiv:1505.02211 [cs.AR], 2015.
%p A011260 with(numtheory): phi(2^n-1)/n;
%t A011260 Table[EulerPhi[(2^n - 1)]/n, {n, 1, 50}]
%o A011260 (PARI) a(n)=eulerphi(2^n-1)/n \\ Hauke Worpel (thebigh(AT)outgun.com), Jun 10 2008
%Y A011260 See A058947 for initial terms.
%Y A011260 Cf. A000010, A000020, A001037, A027695.
%K A011260 nonn,easy,nice
%O A011260 1,3
%A A011260 _N. J. A. Sloane_