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A295849 Number of nonnegative solutions to gcd(x,y,z) = 1 and x^2 + y^2 + z^2 <= n.

%I A295849 #32 Jul 07 2018 04:28:41
%S A295849 0,3,6,7,7,13,16,16,16,19,25,28,28,34,40,40,40,49,52,55,55,61,64,64,
%T A295849 64,70,82,85,85,97,103,103,103,109,118,124,124,130,139,139,139,154,
%U A295849 160,163,163,169,175,175,175,181,193,199,199,211,220,220,220,226,232,241
%N A295849 Number of nonnegative solutions to gcd(x,y,z) = 1 and x^2 + y^2 + z^2 <= n.
%H A295849 Robert Israel, <a href="/A295849/b295849.txt">Table of n, a(n) for n = 0..10000</a>
%F A295849 a(n) = a(n-1) + A295848(n) for n > 0.
%p A295849 N:= 100:
%p A295849 V:= Vector(N):
%p A295849 for x from 0 to floor(sqrt(N/3)) do
%p A295849   for y from x to floor(sqrt((N-x^2)/2)) do
%p A295849     for z from y to floor(sqrt(N-x^2-y^2)) do
%p A295849       if igcd(x,y,z) = 1 then
%p A295849         r:= x^2 + y^2 + z^2;
%p A295849         m:= nops({x,y,z});
%p A295849         if m=3 then V[r]:= V[r]+6
%p A295849         elif m=2 then V[r]:= V[r]+3
%p A295849         else V[r]:= V[r]+1
%p A295849         fi
%p A295849       fi
%p A295849 od od od:
%p A295849 0,op(ListTools:-PartialSums(convert(V,list))); # _Robert Israel_, Nov 30 2017
%t A295849 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]}];
%t A295849 Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Jul 07 2018, after _Andrew Howroyd_ *)
%o A295849 (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
%Y A295849 Cf. A000606, A048134, A295820, A295848.
%K A295849 nonn
%O A295849 0,2
%A A295849 _Seiichi Manyama_, Nov 29 2017