A050465 a(n) = Sum_{d|n, n/d=3 mod 4} d^2.

0, 0, 1, 0, 0, 4, 1, 0, 9, 0, 1, 16, 0, 4, 26, 0, 0, 36, 1, 0, 58, 4, 1, 64, 0, 0, 82, 16, 0, 104, 1, 0, 130, 0, 26, 144, 0, 4, 170, 0, 0, 232, 1, 16, 234, 4, 1, 256, 49, 0, 290, 0, 0, 328, 26, 64, 370, 0, 1, 416, 0, 4, 523, 0, 0, 520, 1, 0, 538, 104, 1, 576, 0

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002117, A027750, A050461, A050470, A076577.

Cf. A050464, A050466, A050467.

Programs

Haskell

a050465 n = sum [d ^ 2 | d <- a027750_row n, mod (div n d) 4 == 3]
-- Reinhard Zumkeller, Mar 06 2012

Mathematica

a[n_] := DivisorSum[n, #^2 &, Mod[n/#, 4] == 3 &]; Array[a, 100] (* Amiram Eldar, Nov 05 2023 *)

PARI

a(n) = sumdiv(n, d, (n/d % 4 == 3) * d^2); \\ Amiram Eldar, Nov 05 2023

Formula

a(n) = A050461(n) - A050470(n). - Reinhard Zumkeller, Mar 06 2012

From Amiram Eldar, Nov 05 2023: (Start)

a(n) = A076577(n) - A050461(n).

a(n) = (A076577(n) - A050470(n))/2.

Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = 7*zeta(3)/16 - Pi^3/64 = 0.041426822002... . (End)

Extensions

Offset fixed by Reinhard Zumkeller, Mar 06 2012