Search: id:A001822
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%I A001822
%S A001822 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,
%T A001822 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,
%U A001822 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
%N A001822 Expansion of Sum x^(3n+2)/(1-x^(3n+2)), n=0..inf.
%C A001822 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
%D A001822 B. C. Berndt,"On a certain theta-function in a letter of Ramanujan from 
               Fitzroy House", Ganita 43 (1992),33-43.
%D A001822 P. G. Dirichlet,"Recherches sur diverses applications de l'analyse infinitesimale 
               a la theorie des nombres", J. Reine Angew. Math. 21 (1840), 1-12.
%H A001822 Nick Hobson, <a href="b001822.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A001822 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%F A001822 Moebius transform is period 3 sequence [0, 1, 0, ...]. - Michael Somos 
               Sep 20 2005
%F A001822 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
%o A001822 (PARI) a(n)=if(n<1, 0, sumdiv(n,d, d%3==2))
%Y A001822 Cf. A001817.
%Y A001822 Sequence in context: A133701 A102442 A091182 this_sequence A112553 A026610 
               A094451
%Y A001822 Adjacent sequences: A001819 A001820 A001821 this_sequence A001823 A001824 
               A001825
%K A001822 nonn
%O A001822 1,8
%A A001822 N. J. A. Sloane (njas(AT)research.att.com).

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