cp's OEIS Frontend

A082050 Sum of divisors of n that are not of the form 3k+1.

%I A082050 #20 Jan 06 2024 09:21:11
%S A082050 0,2,3,2,5,11,0,10,12,7,11,23,0,16,23,10,17,38,0,27,24,13,23,55,5,28,
%T A082050 39,16,29,61,0,42,47,19,40,86,0,40,42,35,41,88,0,57,77,25,47,103,0,57,
%U A082050 71,28,53,119,16,80,60,31,59,153,0,64,96,42,70,121,0,87,95,56,71,190
%N A082050 Sum of divisors of n that are not of the form 3k+1.
%H A082050 Vincenzo Librandi, <a href="/A082050/b082050.txt">Table of n, a(n) for n = 1..10000</a>
%F A082050 a(A004611(n)) = 0.
%F A082050 G.f.: Sum_{k>=1} x^(2*k)*(2+3*x^k+x^(3*k))/(1-x^(3*k))^2. - _Vladeta Jovovic_, Apr 11 2006
%F A082050 Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/18 = 0.548311... (A086463). - _Amiram Eldar_, Jan 06 2024
%t A082050 sd[n_]:=Total[Select[Divisors[n],!IntegerQ[(#-1)/3]&]]; Array[sd,80] (* _Harvey P. Dale_, May 04 2011 *)
%o A082050 (PARI) for(n=1,100,print1(sumdiv(n,d,if(d%3!=1,d))","))
%o A082050 (PARI)
%o A082050 N = 66;  x = 'x + O('x^N);
%o A082050 gf = sum(n=1,N, (3*n-1)*x^(3*n-1)/(1-x^(3*n-1)) + (3*n)*x^(3*n)/(1-x^(3*n)) );
%o A082050 v = Vec(gf);  concat([0],v)
%o A082050 \\ _Joerg Arndt_, May 17 2013
%Y A082050 Cf. A000203, A004611, A027748, A046913, A078181, A078182, A082051, A086463.
%K A082050 nonn,easy
%O A082050 1,2
%A A082050 _Ralf Stephan_, Apr 02 2003