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A000020 Number of primitive polynomials of degree n over GF(2). 9
2, 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)
OFFSET

1,1

COMMENTS

The initial 2 should really be a 1. See A011260 for official version.

REFERENCES

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.

S. V, Duzhin, D. V. Pasechnik, Groups acting on necklaces and sandpile groups, ftp://pdmi.ras.ru/pub/publicat/znsl/v421/p081.pdf, 2014. See p. 92. - N. J. A. Sloane, Jun 30 2014

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.

LINKS

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

MATHEMATICA

Table[If[n==1, 2, EulerPhi[2^n-1]/n], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)

PROG

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

CROSSREFS

Cf. A058947, A011260 (with initial term 1).

Sequence in context: A067541 A054706 A081727 * A077014 A093655 A023140

Adjacent sequences:  A000017 A000018 A000019 * A000021 A000022 A000023

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 26 04:27 EDT 2017. Contains 292502 sequences.