A050462 a(n) = Sum_{d|n, n/d=1 mod 4} d^3.

1, 8, 27, 64, 126, 216, 343, 512, 730, 1008, 1331, 1728, 2198, 2744, 3402, 4096, 4914, 5840, 6859, 8064, 9262, 10648, 12167, 13824, 15751, 17584, 19710, 21952, 24390, 27216, 29791, 32768, 35938, 39312, 43218, 46720, 50654, 54872, 59346

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 Robert G. Wilson v)

Crossrefs

Cf. A007331, A050466, A050471, A175572.

Cf. A050460, A050461, A050463.

Programs

Mathematica

a[n_] := Total[(n/Select[Divisors@ n, Mod[#, 4] == 1 &])^3]; Array[a, 39] (* Robert G. Wilson v, Mar 26 2015 *)
a[n_] := DivisorSum[n, #^3 &, Mod[n/#, 4] == 1 &]; Array[a, 50] (* Amiram Eldar, Nov 05 2023 *)

PARI

a(n) = sumdiv(n, d, ((n/d % 4)== 1)* d^3); \\ Michel Marcus, Mar 26 2015

Formula

From Amiram Eldar, Nov 05 2023: (Start)

a(n) = A007331(n) - A050466(n).

a(n) = A050471(n) + A050466(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 = 1.00181129167264... . (End)

Extensions

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