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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified December 2 02:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)