A050464 a(n) = Sum_{d|n, n/d=3 mod 4} d.

0, 0, 1, 0, 0, 2, 1, 0, 3, 0, 1, 4, 0, 2, 6, 0, 0, 6, 1, 0, 10, 2, 1, 8, 0, 0, 10, 4, 0, 12, 1, 0, 14, 0, 6, 12, 0, 2, 14, 0, 0, 20, 1, 4, 18, 2, 1, 16, 7, 0, 18, 0, 0, 20, 6, 8, 22, 0, 1, 24, 0, 2, 31, 0, 0, 28, 1, 0, 26, 12, 1, 24, 0, 0, 31, 4, 18, 28, 1, 0, 30, 0, 1

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A002131, A050460, A050469, A247037, A326400, A363900.

Cf. A050465, A050466, A050467.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, Mod[n/#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)

PARI

a(n)={sumdiv(n, d, d*(n/d%4==3))} \\ Andrew Howroyd, Sep 13 2019

Formula

G.f.: Sum_{k>=1} k*x^(3*k)/(1 - x^(4*k)). - Ilya Gutkovskiy, Sep 13 2019

G.f.: Sum_{k>0} x^(4*k-1) / (1 - x^(4*k-1))^2. - Seiichi Manyama, Jun 29 2023

from Amiram Eldar, Nov 05 2023: (Start)

a(n) = A002131(n) - A050460(n).

a(n) = A050460(n) - A050469(n).

a(n) = (A002131(n) - A050469(n))/2.

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A247037. (End)

Extensions

Offset changed to 1 by Ilya Gutkovskiy, Sep 13 2019