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%I #19 Nov 26 2023 03:04:54
%S 0,2,0,2,5,2,0,10,0,7,11,2,0,16,5,10,17,2,0,27,0,13,23,10,5,28,0,16,
%T 29,7,0,42,11,19,40,2,0,40,0,35,41,16,0,57,5,25,47,10,0,57,17,28,53,2,
%U 16,80,0,31,59,27,0,64,0,42,70,13,0,87,23,56,71,10,0,76,5,40,88,28,0,115
%N a(n) = Sum_{d|n, d == 2 (mod 3)} d.
%H Seiichi Manyama, <a href="/A078182/b078182.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{n>=0} (3*n+2)*x^(3*n+2)/(1-x^(3*n+2)).
%F A078181(n) + a(n) + 3*A000203(n/3) = A000203(n), where A000203 is defined as zero for non-integer arguments. - _R. J. Mathar_, May 11 2016
%F Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/36 = 0.274155... (A353908). - _Amiram Eldar_, Nov 26 2023
%p A078182 := proc(n)
%p a := 0 ;
%p for d in numtheory[divisors](n) do
%p if modp(d,3) =2 then
%p a :=a+d ;
%p end if;
%p end do:
%p a;
%p end proc: # _R. J. Mathar_, May 11 2016
%t a[n_] := Plus @@ Select[Divisors[n], Mod[#, 3] == 2 &]; Array[a, 100] (* _Giovanni Resta_, May 11 2016 *)
%o (PARI) a(n) = sumdiv(n, d, d*((d%3) == 2)); \\ _Michel Marcus_, May 11 2016
%Y Cf. A001817, A001822, A035386, A078181, A272715, A353908.
%K easy,nonn
%O 1,2
%A _Vladeta Jovovic_, Nov 21 2002
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