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Search: id:A035191
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| A035191 |
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Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 9. |
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+0
6
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| 1, 2, 1, 3, 2, 2, 2, 4, 1, 4, 2, 3, 2, 4, 2, 5, 2, 2, 2, 6, 2, 4, 2, 4, 3, 4, 1, 6, 2, 4, 2, 6, 2, 4, 4, 3, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 5, 3, 6, 2, 6, 2, 2, 4, 8, 2, 4, 2, 6, 2, 4, 2, 7, 4, 4, 2, 6, 2, 8, 2, 4, 2, 4, 3, 6, 4, 4, 2, 10, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of divisors of n not congruent to 0 mod 3. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 26 2001
a(n) is the number of factors (over Q) of the polynomial x^(2n) + x^n + 1 . a(n) = d(3n) - d(n) where d() is the divisor function. - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003
Equals inverse Mobius transform (A051731) of [1, 1, 0, 1, 1, 0, 1, 1, 0,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 24 2009]
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FORMULA
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Multiplicative with a(3^e)=1 and a(p^e)=e+1 for p<>3.
G.f.: Sum_{k>0} x^k*(1+x^k)/(1-x^(3*k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 16 2002
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MAPLE
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for n from 1 to 500 do a := ifactors(n):s := 1:for k from 1 to nops(a[2]) do p := a[2][k][1]:e := a[2][k][2]: if p=3 then b := 1:else b := e+1:fi:s := s*b:od:printf(`%d, `, s); od:
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PROGRAM
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(PARI) direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
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CROSSREFS
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Cf. A035207, A046913, A054584.
Cf. A001227, A000005.
Sequence in context: A033559 A103151 A035221 this_sequence A133924 A023135 A066272
Adjacent sequences: A035188 A035189 A035190 this_sequence A035192 A035193 A035194
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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