A121980 Positive integers z, without duplication, in x^3+y^3=z^2.

1, 3, 4, 8, 13, 24, 27, 28, 32, 49, 64, 81, 98, 104, 108, 125, 147, 168, 181, 189, 192, 216, 224, 228, 256, 312, 343, 351, 361, 375, 388, 392, 500, 507, 512, 525, 549, 588, 648, 671, 676, 729, 756, 784, 832, 847, 864, 1000, 1014, 1029, 1176, 1183, 1225, 1261

Offset: 1

Author

R. J. Mathar, Sep 11 2006

Keywords

• nonn

Comments

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.

Examples

			(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),
(8,8,32),(-7,14,49),(0,16,64),(9,18,81),(7,21,98),(-28,32,104).
		

Crossrefs

Cf. A103254, A103255.