A392776 - OEIS

A392776

a(n) is the number of solutions of (x^2+y^2+z^2)/(x*y + x*z + y*z) = A331605(n), such that 0 < |x| <= |y| <= z <= A331605(n), gcd(|x|,|y|,z) = 1.

1, 0, 1, 1, 2, 1, 1, 2, 2, 3, 4, 1, 2, 2, 2, 4, 1, 2, 4, 1, 2, 3, 2, 3, 4, 4, 6, 3, 2, 2, 2, 4, 2, 2, 1, 8, 2, 2, 2, 4, 6, 4, 9, 2, 2, 2, 2, 6, 4, 18, 1, 2, 4, 4, 2, 4, 4, 2, 8, 2, 2, 1, 2, 11, 6, 4, 2, 4, 4, 2, 2, 2, 5, 3, 4, 8, 1, 8, 8, 4, 4, 4, 2, 3, 2

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OFFSET

1,5

COMMENTS

It appears that a(n) > 0, n > 2; i.e., if there exist unbounded solutions for some n > 2, then the bounded one exists too.

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

a(1) = 1, solution is (1,1,1).

a(2) = 0, as potential solutions (0,1,1) and (1,1,4) are out of the bounds.

a(11) = 4, solutions are (-2,3,7), (-2,3,55), (-5,7,22), (-17,30,43), A331605(11) = 62.

CROSSREFS