A228880 Numbers of the form x^2*y*(2*x + y).

0, 3, 8, 15, 20, 24, 35, 48, 63, 80, 84, 99, 120, 128, 143, 144, 168, 180, 195, 224, 240, 243, 255, 275, 288, 308, 320, 323, 360, 384, 399, 440, 468, 483, 495, 528, 560, 575, 600, 624, 648, 660, 675, 728, 735, 768, 783, 819, 840, 884, 899, 960, 975, 1008

Offset

1,2

Comments

(y^2 + 2*x*y - x^2)^4 + (2*x + y)*x^2*y*(2*x + 2*y)^4 = (x^4 + y^4 + 10*x^2*y^2 + 4*x*y^3 + 13*x^3*y)^2. The equation implies that for any n, x^4 + a(n)*y^4 = z^2 is solvable in integers.

References

L. E. Dickson, History of the Theory of Numbers, Vol. II. Diophantine analysis, Carnegie Institute of Washington, 1919. Reprinted by AMS Chelsea Publishing, New York, 1992, p. 631.

Links

Table of n, a(n) for n=1..54.

Mathematica

n = 1008; limx = Floor[(n/2)^(1/3)]; limy = Floor@Sqrt[n]; Select[Union@Flatten@Table[x^2*y*(2*x + y), {x, 0, limx}, {y, limy}], # <= n &]

Crossrefs

Cf. A218381.

Sequence in context: A310312 A310313 A213158 * A310314 A181027 A060320

Adjacent sequences: A228877 A228878 A228879 * A228881 A228882 A228883

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 11 2013

Status

approved