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A295849 Number of nonnegative solutions to gcd(x,y,z) = 1 and x^2 + y^2 + z^2 <= n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = a(n-1) + A295848(n) for n > 0.

MAPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A000606, A048134, A295820, A295848.

Sequence in context: A152083 A251532 A251533 * A003458 A133339 A112267

Adjacent sequences:  A295846 A295847 A295848 * A295850 A295851 A295852

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Nov 29 2017

STATUS

approved

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Last modified May 19 17:48 EDT 2019. Contains 323395 sequences. (Running on oeis4.)