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A001822
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Expansion of Sum x^(3n+2)/(1-x^(3n+2)), n=0..inf.
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6
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0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 3, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 0, 3, 1, 2, 2, 1, 0, 2, 0, 4, 1, 2, 0, 3, 1, 2, 1, 2, 0, 3, 1, 2, 1, 1, 2, 4, 0, 2, 1, 3, 0, 2, 0, 3, 2, 2, 0, 3, 1, 4, 1, 2, 0, 2, 1, 2, 2, 2, 0, 5, 0, 2, 1, 2, 2, 2, 1, 4, 1, 2, 0, 3, 0, 2, 2, 3, 0, 3, 1, 4, 1, 2, 0, 4, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| a(n) is the number of positive divisors of n of the form 3k+2. If r(n) denotes the number of representations of n by the quadratic form j^2+ij+i^2, then r(n)= 6 *(A001817(n)-a(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2002
a(n) = (A035191(n) - A002324(n)) / 2. [Reinhard Zumkeller, Nov 26 2011]
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REFERENCES
| B. C. Berndt,"On a certain theta-function in a letter of Ramanujan from Fitzroy House", Ganita 43 (1992),33-43.
P. G. Dirichlet,"Recherches sur diverses applications de l'analyse infinitesimale a la theorie des nombres", J. Reine Angew. Math. 21 (1840), 1-12.
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LINKS
| Nick Hobson, Table of n, a(n) for n = 1..10000
Michael Gilleland, Some Self-Similar Integer Sequences
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FORMULA
| Moebius transform is period 3 sequence [0, 1, 0, ...]. - Michael Somos Sep 20 2005
G.f.: Sum_{k>0} x^(3k-1)/(1-x^(3k-1)) = Sum_{k>0} x^(2k)/(1-x^(3k)) . - Michael Somos Sep 20 2005
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PROG
| (PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%3==2))
(Haskell)
a001822 n = length [d | d <- [2, 5..n], mod n d == 0]
-- Reinhard Zumkeller, Nov 26 2011
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CROSSREFS
| Cf. A001817.
Sequence in context: A133701 A102442 A091182 * A112553 A026610 A094451
Adjacent sequences: A001819 A001820 A001821 * A001823 A001824 A001825
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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