A093836 Numerator of A000328(n)/n^2, where A000328(n) is the number of lattice points (x,y) with x^2 + y^2 <= n^2.

5, 13, 29, 49, 81, 113, 149, 197, 253, 317, 377, 49, 529, 613, 709, 797, 53, 1009, 1129, 1257, 1373, 1517, 1653, 1793, 1961, 2121, 763, 2453, 2629, 2821, 3001, 3209, 3409, 3625, 3853, 1351, 4293, 4513, 4777, 201, 5261, 5525, 5789, 6077, 6361, 6625

Offset: 1

Author

Eric W. Weisstein, Apr 17 2004

Keywords

• nonn
• frac

Comments

First differs from A000328 at n=12: A000328(12) = 441, a(12) = 49.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Gauss's Circle Problem

Crossrefs

Cf. A093837 (denominators), A000328, A093832.

Programs

Maple

N:= 100: # to get a(1) to a(N)
B:= Array(1..N);
for i from 0 to N do
  for j from i while i^2 + j^2 <= N^2 do
     v:= ceil(sqrt(i^2+j^2));
     if [i,j] = [0,0] then m:= 1; v:= 1
     elif i=0 or i=j then m:= 4
     else m:= 8
     fi;
     B[v]:= B[v]+m;
  od
od:
A000328:= ListTools:-PartialSums(convert(B,list)):
seq(numer(A000328[n]/n^2),n=1..N); # Robert Israel, May 28 2015

Extensions

Definition edited by Robert Israel, May 28 2015