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A295820
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Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 <= n.
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4
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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
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = a(n-1) + A295819(n) for n > 0.
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = {sum(i=0, sqrtint(n), sum(j=0, sqrtint(n-i^2), gcd(i, j) == 1))} \\ Andrew Howroyd, Dec 12 2017
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CROSSREFS
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Cf. A049643, A224212, A295819, A295849.
Sequence in context: A284397 A284374 A137847 * A164023 A097224 A087418
Adjacent sequences: A295817 A295818 A295819 * A295821 A295822 A295823
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Nov 28 2017
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STATUS
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approved
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