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Search: id:A001817
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| A001817 |
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G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum x^(3n+1)/(1-x^(3n+1)), n=0..inf. |
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+0
4
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| 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 4, 1, 2, 2, 3, 1, 2, 1, 3, 3, 3, 1, 4, 1, 1, 2, 4, 2, 2, 1, 3, 2, 2, 2, 4, 2, 2, 2, 3, 1, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 5, 1, 2, 1, 4, 2, 2, 1, 4, 1, 2, 4, 3, 2, 2, 2, 3, 2, 3, 1, 5, 1, 2, 2, 4, 2
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n) is the number of positive divisors of n of the form 3k+1. If r(n) denotes the number of representations of n by the quadratic form j^2+ij+i^2, then r(n)= 6 *(a(n)-A001822(n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2002
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REFERENCES
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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
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Nick Hobson, Table of n, a(n) for n = 1..10000
Michael Gilleland, Some Self-Similar Integer Sequences
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FORMULA
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Moebius transform is period 3 sequence [1, 0, 0, ...]. - Michael Somos Sep 20 2005
G.f.: Sum_{k>0} x^(3k-2)/(1-x^(3k-2)) = Sum_{k>0} x^k/(1-x^(3k)) . - Michael Somos Sep 20 2005
Equals A051731 * [1, 0, 0, 1, 0, 0, 1, 0, 0, 1,...], where A051731 is the inverse Mobius transform. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 06 2007
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EXAMPLE
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x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + x^9 + ...
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d%3==1))
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CROSSREFS
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Cf. A001822.
Cf. A051731.
Sequence in context: A100428 A093914 A007061 this_sequence A091954 A080236 A025142
Adjacent sequences: A001814 A001815 A001816 this_sequence A001818 A001819 A001820
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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