A078182 a(n) = Sum_{d|n, d == 2 (mod 3)} d.

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, 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, 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

Offset: 1

Author

Vladeta Jovovic, Nov 21 2002

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001817, A001822, A035386, A078181, A272715, A353908.

Programs

Maple

A078182 := proc(n)
    a := 0 ;
    for d in numtheory[divisors](n) do
        if modp(d,3) =2 then
            a :=a+d ;
        end if;
    end do:
    a;
end proc: # R. J. Mathar, May 11 2016

Mathematica

a[n_] := Plus @@ Select[Divisors[n], Mod[#, 3] == 2 &]; Array[a, 100] (* Giovanni Resta, May 11 2016 *)

PARI

a(n) = sumdiv(n, d, d*((d%3) == 2)); \\ Michel Marcus, May 11 2016

Formula

G.f.: Sum_{n>=0} (3*n+2)*x^(3*n+2)/(1-x^(3*n+2)).

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

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