A050467 a(n) = Sum_{d|n, n/d=3 mod 4} d^4.

0, 0, 1, 0, 0, 16, 1, 0, 81, 0, 1, 256, 0, 16, 626, 0, 0, 1296, 1, 0, 2482, 16, 1, 4096, 0, 0, 6562, 256, 0, 10016, 1, 0, 14722, 0, 626, 20736, 0, 16, 28562, 0, 0, 39712, 1, 256, 50706, 16, 1, 65536, 2401, 0, 83522, 0, 0, 104992, 626, 4096, 130402

Offset: 1

Author

N. J. A. Sloane, Dec 23 1999

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A013663, A050463, A050468, A285989.

Cf. A050464, A050465, A050466.

Programs

Mathematica

Table[Total[Select[Divisors[n],Mod[n/#,4]==3&]^4],{n,60}] (* Harvey P. Dale, Jun 10 2023 *)
a[n_] := DivisorSum[n, #^4 &, Mod[n/#, 4] == 3 &]; Array[a, 50] (* Amiram Eldar, Nov 05 2023 *)

PARI

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

Formula

From Amiram Eldar, Nov 05 2023: (Start)

a(n) = A285989(n) - A050463(n).

a(n) = A050463(n) - A050468(n).

a(n) = (A285989(n) - A050468(n))/2.

Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = 31*zeta(5)/64 - 5*Pi^5/3072 = 0.00418296735902... . (End)

Extensions

Offset corrected by Amiram Eldar, Nov 05 2023