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A295849
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Number of nonnegative solutions to gcd(x,y,z) = 1 and x^2 + y^2 + z^2 <= n.
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3
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0, 3, 6, 7, 7, 13, 16, 16, 16, 19, 25, 28, 28, 34, 40, 40, 40, 49, 52, 55, 55, 61, 64, 64, 64, 70, 82, 85, 85, 97, 103, 103, 103, 109, 118, 124, 124, 130, 139, 139, 139, 154, 160, 163, 163, 169, 175, 175, 175, 181, 193, 199, 199, 211, 220, 220, 220, 226, 232, 241
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..10000
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FORMULA
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a(n) = a(n-1) + A295848(n) for n > 0.
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MAPLE
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N:= 100:
V:= Vector(N):
for x from 0 to floor(sqrt(N/3)) do
for y from x to floor(sqrt((N-x^2)/2)) do
for z from y to floor(sqrt(N-x^2-y^2)) do
if igcd(x, y, z) = 1 then
r:= x^2 + y^2 + z^2;
m:= nops({x, y, z});
if m=3 then V[r]:= V[r]+6
elif m=2 then V[r]:= V[r]+3
else V[r]:= V[r]+1
fi
fi
od od od:
0, op(ListTools:-PartialSums(convert(V, list))); # Robert Israel, Nov 30 2017
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MATHEMATICA
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a[n_] := Sum[Boole[GCD[i, j, k] == 1], {i, 0, Sqrt[n]}, {j, 0, Sqrt[n - i^2]}, {k, 0, Sqrt[n - i^2 - j^2]}];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jul 07 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), sum(k=0, sqrtint(n-i^2-j^2), gcd([i, j, k]) == 1)))} \\ Andrew Howroyd, Dec 12 2017
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CROSSREFS
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Cf. A000606, A048134, A295820, A295848.
Sequence in context: A152083 A251532 A251533 * A003458 A133339 A112267
Adjacent sequences: A295846 A295847 A295848 * A295850 A295851 A295852
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Nov 29 2017
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STATUS
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approved
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