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%I #3 Mar 30 2012 17:39:13
%S 1,3,4,8,13,24,27,28,32,49,64,81,98,104,108,125,147,168,181,189,192,
%T 216,224,228,256,312,343,351,361,375,388,392,500,507,512,525,549,588,
%U 648,671,676,729,756,784,832,847,864,1000,1014,1029,1176,1183,1225,1261
%N Positive integers z, without duplication, in x^3+y^3=z^2.
%C The first duplicate is (-23,71,588),(14,70,588), the second (-119,140,1029),(49,98,1029). A033430(m) and A000578(k) are subsets since (x,y,z)=(2m,2m,4m^3) or (x,y,z)=(0,k^2,k^3) solve x^3+y^3=z^2. The "leakage" problem of A103254 can be avoided by introducing s=x+y and d=y-x and searching for solutions of the transformed equation s(s^2+3d^2)=4z^2 over all positive divisors s of 4z^2.
%e (x,y,z)=(0,1,1),(1,2,3),(2,2,4),(0,4,8),(-7,8,13),(4,8,24),(0,9,27),(-6,10,28),
%e (8,8,32),(-7,14,49),(0,16,64),(9,18,81),(7,21,98),(-28,32,104).
%Y Cf. A103254, A103255.
%K nonn
%O 1,2
%A _R. J. Mathar_, Sep 11 2006
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