OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Wikipedia, Gauss circle problem
J. Wu, On the primitive circle problem, Monatsh. Math. 135 (2002), 69.
W. G. Zhai and X.D. Cao, On the number of coprime integer pairs within a circle, Acta Arith. 90 (1999), 1.
FORMULA
a(n) = 4*A176562(n). - R. J. Mathar, May 07 2010
a(n) = A304651(n^2). - Seiichi Manyama, May 26 2018
EXAMPLE
a(2) = 8 counts (x,y) = (-1,-1), (-1,0), (-1,1), (0,-1), (0,1), (1,-1), (1,0) and (1,1).
MATHEMATICA
a89[n_] := a89[n] = Product[{p, e} = pe; Which[p < 3 && e == 1, 1, p == 2 && e > 1, 0, Mod[p, 4] == 1, 2, Mod[p, 4] == 3, 0, True, a89[p^e]], {pe, FactorInteger[n]}];
b[n_] := b[n] = If[n == 0, 0, b[n-1] + 4 a89[n]];
a[n_] := b[n^2];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 02 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Apr 16 2010
STATUS
approved