Search: id:A001817
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%I A001817
%S A001817 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,
%T A001817 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,
%U A001817 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
%N A001817 G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum x^(3n+1)/(1-x^(3n+1)), n=0..inf.
%C A001817 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
%D A001817 B. C. Berndt,"On a certain theta-function in a letter of Ramanujan from 
               Fitzroy House", Ganita 43 (1992),33-43.
%D A001817 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 A001817 Nick Hobson, <a href="b001817.txt">Table of n, a(n) for n = 1..10000</
               a>
%H A001817 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%F A001817 Moebius transform is period 3 sequence [1, 0, 0, ...]. - Michael Somos 
               Sep 20 2005
%F A001817 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
%F A001817 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
%e A001817 x + x^2 + x^3 + 2*x^4 + x^5 + x^6 + 2*x^7 + 2*x^8 + x^9 + ...
%o A001817 (PARI) a(n)=if(n<1,0,sumdiv(n,d,d%3==1))
%Y A001817 Cf. A001822.
%Y A001817 Cf. A051731.
%Y A001817 Sequence in context: A100428 A093914 A007061 this_sequence A091954 A080236 
               A025142
%Y A001817 Adjacent sequences: A001814 A001815 A001816 this_sequence A001818 A001819 
               A001820
%K A001817 nonn
%O A001817 1,4
%A A001817 N. J. A. Sloane (njas(AT)research.att.com).

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