A295820 Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 <= n.

0, 2, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 13, 15, 15, 15, 17, 17, 17, 17, 17, 19, 19, 19, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 27, 27, 27, 27, 27, 29, 29, 29, 31, 31, 31, 31, 35, 35, 35, 35, 35, 35

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = a(n-1) + A295819(n) for n > 0.

Example

Solutions to (x,y) = 1 and x^2 + y^2 <= 17;
  *         (1,4)
  * *       (1,3), (2,3)
  *   *     (1,2), (3,2)
* * * * *   (0,1), (1,1), (2,1), (3,1), (4,1)
  *         (1,0)
            a(17) = 11.

Mathematica

a[n_] := Sum[Boole[GCD[i, j]==1 ], {i, 0, Sqrt[n]}, {j, 0, Sqrt[n-i^2]}];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 05 2018, after Andrew Howroyd *)

Prog

(PARI) a(n) = {sum(i=0, sqrtint(n), sum(j=0, sqrtint(n-i^2), gcd(i, j) == 1))} \\ Andrew Howroyd, Dec 12 2017

Crossrefs

Cf. A049643, A224212, A295819, A295849.

Sequence in context: A284397 A284374 A137847 * A164023 A097224 A087418

Adjacent sequences: A295817 A295818 A295819 * A295821 A295822 A295823

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2017

Status

approved