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A295819 Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 = n. 4
0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = A000089(n) for n >= 2.

a(A006278(n)) = 2^n for n >= 1.

EXAMPLE

a(1) = 2;

(1,0) = 1 and 1^2 + 0^2 =  1.

(0,1) = 1 and 0^2 + 1^2 =  1.

a(2) = 1;

(1,1) = 1 and 1^2 + 1^2 =  2. ->  1^2 +  1^2 == 1^2 + 1 == 0 mod  2.

a(5) = 2;

(2,1) = 1 and 2^2 + 1^2 =  5. ->  2^2 +  1^2 == 2^2 + 1 == 0 mod  5.

(1,2) = 1 and 1^2 + 2^2 =  5. ->  3^2 +  6^2 == 3^2 + 1 == 0 mod  5.

a(10) = 2;

(3,1) = 1 and 3^2 + 1^2 = 10. ->  3^2 +  1^2 == 3^2 + 1 == 0 mod 10.

(1,3) = 1 and 1^2 + 3^2 = 10. ->  7^2 + 21^2 == 7^2 + 1 == 0 mod 10.

a(13) = 2;

(3,2) = 1 and 3^2 + 2^2 = 13. -> 21^2 + 14^2 == 8^2 + 1 == 0 mod 13.

(2,3) = 1 and 2^2 + 3^2 = 13. -> 18^2 + 27^2 == 5^2 + 1 == 0 mod 13.

MATHEMATICA

a[n_] := Sum[j = Sqrt[n - i^2] // Floor; Boole[GCD[i, j] == 1 && i^2 + j^2 == n], {i, 0, Sqrt[n]}];

Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Jul 05 2018, after Andrew Howroyd *)

PROG

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

CROSSREFS

Cf. A006278.

Similar sequences: A000010, A000925, A295820, A295848, A295976.

A000089 is essentially the same sequence.

Sequence in context: A110855 A054673 A155103 * A048105 A335021 A176202

Adjacent sequences:  A295816 A295817 A295818 * A295820 A295821 A295822

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 28 2017

STATUS

approved

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Last modified May 25 06:43 EDT 2022. Contains 354049 sequences. (Running on oeis4.)