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A062692
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Number of irreducible polynomials over F_2 of degree at most n.
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4
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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
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OFFSET
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1,1
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REFERENCES
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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.
M. Waldschmidt, Lectures on Multiple Zeta Values (IMSC 2011), http://www.math.jussieu.fr/~miw/articles/pdf/MZV2011IMSc.pdf
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LINKS
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Table of n, a(n) for n=1..34.
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FORMULA
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Sum_{m=1..n} 1/m sum_{d | m } mu(d)*2^{m/d}.
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MAPLE
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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);
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PROG
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(PARI) a(n)=sum(m=1, n, 1/m* sumdiv(m, d, moebius(d)*2^(m/d) ) ); /* Joerg Arndt, Jul 04 2011 */
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CROSSREFS
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Partial sums of A001037.
a(n) = A091226(2^(n+1)). Cf. A014580, A091231.
Equals A001036 + 1.
Sequence in context: A191794 A191388 A194850 * A182024 A018154 A127603
Adjacent sequences: A062689 A062690 A062691 * A062693 A062694 A062695
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KEYWORD
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nonn,easy
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AUTHOR
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Gary L Mullen (mullen(AT)math.psu.edu), Jul 04 2001
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EXTENSIONS
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More terms from Sascha Kurz, Mar 25 2002
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STATUS
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approved
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