A082051 - OEIS

%I #17 Jan 06 2024 09:21:15

%S 1,1,4,5,1,10,8,5,13,11,1,26,14,8,19,21,1,37,20,15,32,23,1,50,26,14,

%T 40,40,1,65,32,21,37,35,8,89,38,20,56,55,1,80,44,27,73,47,1,114,57,36,

%U 55,70,1,118,56,40,80,59,1,141,62,32,104,85,14,131,68,39,73,88,1,185

%N Sum of divisors of n that are not of the form 3k+2.

%H Vincenzo Librandi, <a href="/A082051/b082051.txt">Table of n, a(n) for n = 1..10000</a>

%F a(A003627(n)) = 1.

%F G.f.: Sum_{k>=1} x^k*(1 + 3*x^(2*k) + 2*x^(3*k))/(1 - x^(3*k))^2. - _Ilya Gutkovskiy_, Sep 12 2019

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/18 = 0.548311... (A086463). - _Amiram Eldar_, Jan 06 2024

%t sd[n_]:= Total[Select[Divisors[n], !IntegerQ[(# - 2) / 3]&]]; Array[sd, 100] (* _Vincenzo Librandi_, May 17 2013 *)

%o (PARI) for(n=1,100,print1(sumdiv(n,d,if(d%3!=2,d))","))

%o (PARI)

%o N = 66;  x = 'x + O('x^N);

%o gf = sum(n=1,N, (3*n-2)*x^(3*n-2)/(1-x^(3*n-2)) + (3*n)*x^(3*n)/(1-x^(3*n)) );

%o v = Vec(gf)

%o \\ _Joerg Arndt_, May 17 2013

%Y Cf. A000203, A003627, A027748, A046913, A078181, A078182, A082050, A086463, A326394.

%K nonn,easy

%O 1,3

%A _Ralf Stephan_, Apr 02 2003