A327337 Consider primitive solutions (x,y,z) to the system x+y+z = r^2, x^2+y^2+z^2 = s^2, x^3+y^3+z^3 = t^2, with 0<x<=y<=z arranged in order of increasing z; sequence gives z values.

129, 2873, 92218, 101464, 252092, 322966, 732516

Offset

1,1

Comments

A solution is primitive if it cannot be obtained multiplying another solution by a square greater than 1, i.e., if GCD(x,y,z) is squarefree.

The first two solutions are reported in Choudhry's paper, whose main purpose is providing a parametric solution.

Links

Table of n, a(n) for n=1..7.

Ajai Choudhry, A diophantine system, arXiv:1908.09742v1 [math.NT], 2019.

Example

108 + 124 + 129 = 19^2, 108^2 + 124^2 + 129^2 = 209^2, 108^3 + 124^3 + 129^3 = 2305^2.

Crossrefs

The corresponding x and y values are in A327338 and A327339.

Cf. A139266.

Sequence in context: A301551 A297493 A279640 * A305722 A189608 A168067

Adjacent sequences: A327334 A327335 A327336 * A327338 A327339 A327340

Keyword

nonn,more

Author

Giovanni Resta, Sep 02 2019

Status

approved