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A228880
Numbers of the form x^2*y*(2*x + y).
1
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved