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A050464
a(n) = Sum_{d|n, n/d=3 mod 4} d.
7
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
1,6
LINKS
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)
MATHEMATICA
a[n_] := DivisorSum[n, # &, Mod[n/#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Jun 27 2023 *)
PROG
(PARI) a(n)={sumdiv(n, d, d*(n/d%4==3))} \\ Andrew Howroyd, Sep 13 2019
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 23 1999
EXTENSIONS
Offset changed to 1 by Ilya Gutkovskiy, Sep 13 2019
STATUS
approved