A048155 a(n)=Sum{T(n,k): k=1,2,...,n}, array T as in A048154.

0, 1, 3, 4, 10, 15, 21, 16, 27, 45, 55, 60, 78, 91, 105, 96, 136, 135, 171, 180, 210, 231, 253, 240, 250, 325, 243, 364, 406, 435, 465, 384, 528, 561, 595, 540, 666, 703, 741, 720, 820, 861, 903, 924, 945, 1035, 1081, 1056, 1029

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..5000

Formula

a(n) = Sum_{k=1..n} k*(1-floor(k^3/n)+floor((k^3 -1)/n)). - Anthony Browne, Jun 26 2016

Example

a(3) = 3 since (1^3 mod 3) + (2^3 mod 3) + (3^3 mod 3) = (1 mod 3) + (8 mod 3) + (27 mod 3) = 1 + 2 + 0 = 3.

Mathematica

Table[Sum[Mod[k^3, n], {k, n}], {n, 50}] (* or *)
Table[Sum[k (1 - Floor[k^3/n] + Floor[(k^3 - 1)/n]), {k, n}], {n, 50}] (* Michael De Vlieger, Jun 26 2016 *)

Crossrefs

Cf. A048154.

Sequence in context: A285042 A319719 A347568 * A242342 A204292 A218277

Adjacent sequences: A048152 A048153 A048154 * A048156 A048157 A048158

Keyword

nonn

Author

Clark Kimberling

Status

approved