|
%I #13 Jun 28 2016 23:31:24
%S 0,1,3,4,10,15,21,16,27,45,55,60,78,91,105,96,136,135,171,180,210,231,
%T 253,240,250,325,243,364,406,435,465,384,528,561,595,540,666,703,741,
%U 720,820,861,903,924,945,1035,1081,1056,1029
%N a(n)=Sum{T(n,k): k=1,2,...,n}, array T as in A048154.
%H Michael De Vlieger, <a href="/A048155/b048155.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = Sum_{k=1..n} k*(1-floor(k^3/n)+floor((k^3 -1)/n)). - _Anthony Browne_, Jun 26 2016
%e 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.
%t Table[Sum[Mod[k^3, n], {k, n}], {n, 50}] (* or *)
%t Table[Sum[k (1 - Floor[k^3/n] + Floor[(k^3 - 1)/n]), {k, n}], {n, 50}] (* _Michael De Vlieger_, Jun 26 2016 *)
%Y Cf. A048154.
%K nonn
%O 1,3
%A _Clark Kimberling_
|
