A050466 a(n) = Sum_{d|n, n/d=3 mod 4} d^3.

0, 0, 1, 0, 0, 8, 1, 0, 27, 0, 1, 64, 0, 8, 126, 0, 0, 216, 1, 0, 370, 8, 1, 512, 0, 0, 730, 64, 0, 1008, 1, 0, 1358, 0, 126, 1728, 0, 8, 2198, 0, 0, 2960, 1, 64, 3402, 8, 1, 4096, 343, 0, 4914, 0, 0, 5840, 126, 512, 6886, 0, 1, 8064, 0, 8, 9991, 0

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Comments

From Robert G. Wilson v, Mar 26 2015: (Start)

a(n) = 0 for n = 1, 2, 4, 5, 8, 10, 13, 16, 17, 20, 25, ... (A072437).

a(n) = 1 for n = 3, 7, 11, 19, 23, 31, 43, 47, 59, 67, ... (A002145). (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert G. Wilson v)

Crossrefs

Cf. A007331, A050462, A050471, A175572.

Cf. A050464, A050465, A050467.

Cf. A002145, A072437.

Programs

Mathematica

a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 3 &])^3]; Array[a, 64] (* Robert G. Wilson v, Mar 26 2015 *)
a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 3 &]; Array[a, 50] (* Amiram Eldar, Nov 05 2023 *)

PARI

a(n) = sumdiv(n, d, ((n/d % 4)== 3)* d^3); \\ Michel Marcus, Mar 26 2015

Formula

From Amiram Eldar, Nov 05 2023: (Start)

a(n) = A007331(n) - A050462(n).

a(n) = A050462(n) - A050471(n).

a(n) = (A007331(n) - A050471(n))/2.

Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = Pi^4/192 - A175572/2 = 0.0128667399315... . (End)

Extensions

Offset changed from 0 to 1 by Robert G. Wilson v, Mar 27 2015