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 A295820 Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 <= n. 4

%I #26 Jul 05 2018 09:10:46

%S 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,

%T 15,17,17,17,17,17,19,19,19,21,21,21,21,23,23,23,23,23,23,23,23,23,25,

%U 25,25,27,27,27,27,27,29,29,29,31,31,31,31,35,35,35,35,35,35

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

%H Seiichi Manyama, <a href="/A295820/b295820.txt">Table of n, a(n) for n = 0..1000</a>

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

%e Solutions to (x,y) = 1 and x^2 + y^2 <= 17;

%e * (1,4)

%e * * (1,3), (2,3)

%e * * (1,2), (3,2)

%e * * * * * (0,1), (1,1), (2,1), (3,1), (4,1)

%e * (1,0)

%e a(17) = 11.

%t a[n_] := Sum[Boole[GCD[i, j]==1 ], {i, 0, Sqrt[n]}, {j, 0, Sqrt[n-i^2]}];

%t Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Jul 05 2018, after _Andrew Howroyd_ *)

%o (PARI) a(n) = {sum(i=0, sqrtint(n), sum(j=0, sqrtint(n-i^2), gcd(i, j) == 1))} \\ _Andrew Howroyd_, Dec 12 2017

%Y Cf. A049643, A224212, A295819, A295849.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 28 2017

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Last modified September 19 14:43 EDT 2024. Contains 376013 sequences. (Running on oeis4.)