login
A050462
a(n) = Sum_{d|n, n/d=1 mod 4} d^3.
5
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
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Robert G. Wilson v)
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)
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 *)
PROG
(PARI) a(n) = sumdiv(n, d, ((n/d % 4)== 1)* d^3); \\ Michel Marcus, Mar 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 23 1999
EXTENSIONS
Offset changed from 0 to 1 by Robert G. Wilson v, Mar 27 2015
STATUS
approved