A304651 Number of coprime pairs (x,y) with x^2 + y^2 <= n.

0, 4, 8, 8, 8, 16, 16, 16, 16, 16, 24, 24, 24, 32, 32, 32, 32, 40, 40, 40, 40, 40, 40, 40, 40, 48, 56, 56, 56, 64, 64, 64, 64, 64, 72, 72, 72, 80, 80, 80, 80, 88, 88, 88, 88, 88, 88, 88, 88, 88, 96, 96, 96, 104, 104, 104, 104, 104, 112, 112, 112, 120, 120, 120, 120

Offset: 0

Author

Seiichi Manyama, May 26 2018

Keywords

• nonn

Examples

			a(2) = 8 counts (x,y) = (-1,-1), (-1,0), (-1,1), (0,-1), (0,1), (1,-1), (1,0) and (1,1).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000089, A175341, A305117.

Programs

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]}];
a[n_] := a[n] = If[n == 0, 0, a[n-1] + 4 a89[n]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Aug 02 2023 *)

Formula

a(n) = a(n-1) + 4*A000089(n) for n > 0.