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A062692 Number of irreducible polynomials over F_2 of degree at most n. 7
2, 3, 5, 8, 14, 23, 41, 71, 127, 226, 412, 747, 1377, 2538, 4720, 8800, 16510, 31042, 58636, 111013, 210871, 401428, 766150, 1465020, 2807196, 5387991, 10358999, 19945394, 38458184, 74248451, 143522117, 277737797, 538038783, 1043325198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Number of binary pre-necklaces of length n. [Joerg Arndt, Jul 20 2013]

REFERENCES

Hicks, Kenneth H.; Mullen, Gary L.; and Sato, Ikuro, Distribution of irreducible polynomials over F_2, in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (Oaxaca, 2001), 177-186, Springer, Berlin, 2002.

LINKS

Table of n, a(n) for n=1..34.

G. Fici and Zs. Lipták, On Prefix Normal Words.

G. Fici and Zs. Lipták, On Prefix Normal Words, Developments in Language Theory 2011, Lecture Notes in Computer Science 6795, 228-238.

M. Waldschmidt, Lectures on Multiple Zeta Values, IMSC 2011.

FORMULA

a(n) = Sum_{m=1..n} 1/m sum_{d | m } mu(d)*2^{m/d}.

MAPLE

with(numtheory):for n from 1 to 113 do sum3 := 0:for m from 1 to n do sum2 := 0:a := divisors(m):for h from 1 to nops(a) do sum2 := sum2+mobius(a[h])*2^(m/a[h]):end do:sum3 := sum3+sum2/m:end do:s[n] := sum3:end do:q := seq(s[j], j=1..113);

MATHEMATICA

a[n_] := Sum[1/m DivisorSum[m, MoebiusMu[#]*2^(m/#)&], {m, 1, n}]; Array[a, 34] (* Jean-François Alcover, Dec 07 2015 *)

PROG

(PARI) a(n)=sum(m=1, n, 1/m* sumdiv(m, d, moebius(d)*2^(m/d) ) ); /* Joerg Arndt, Jul 04 2011 */

CROSSREFS

Partial sums of A001037.

a(n) = A091226(2^(n+1)). Cf. A014580, A091231.

Equals A001036 + 1.

Column k=2 of A143328. - Alois P. Heinz, Jul 20 2013

Sequence in context: A191794 A191388 A194850 * A182024 A086661 A018154

Adjacent sequences:  A062689 A062690 A062691 * A062693 A062694 A062695

KEYWORD

nonn,easy

AUTHOR

Gary L Mullen (mullen(AT)math.psu.edu), Jul 04 2001

EXTENSIONS

More terms from Sascha Kurz, Mar 25 2002

STATUS

approved

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Last modified December 2 19:13 EST 2016. Contains 278683 sequences.