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 A062692 Number of irreducible polynomials over F_2 of degree at most n. 8
 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 Peter Burcsi, G Fici, Z Lipták, F Ruskey, J Sawada, On prefix normal words and prefix normal forms, Preprint, 2016; http://www.cis.uoguelph.ca/~sawada/papers/pnf.pdf 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 G. C. Greubel, Table of n, a(n) for n = 1..3320 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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