A295819 Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 = n.
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
Offset: 0
Keywords
Examples
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.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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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-François Alcover, Jul 05 2018, after Andrew Howroyd *) -
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