A272023 Numbers n such that n^3 = (x^3 + y^3 + z^3) / 3 where x > y > z > 0, is soluble.

75, 87, 126, 135, 150, 171, 174, 204, 225, 246, 252, 261, 270, 297, 300, 333, 342, 348, 375, 378, 405, 408, 435, 450, 457, 492, 504, 513, 522, 525, 540, 543, 594, 600, 609, 612, 618, 630, 645, 666, 675, 684, 696, 723, 738, 741, 750, 753, 756, 783, 788, 810, 813, 815, 816, 825, 855, 870, 882, 891, 900, 914

Offset: 1

Author

Altug Alkan, Apr 18 2016

Keywords

• nonn

Comments

Numbers whose cube is the average of three distinct positive cubes.

If n is in this sequence, then k*n is also a member of this sequence for all k > 0.

Terms that are not divisible by 3 are 457, 788, 815, 914, ...

Terms that are not members of A023042 are 457, 914, 1078, ...

Examples

			75 is a term because 75^3 = (10^3 + 17^3 + 108^3) / 3.
150 = 2*75 is a term.
87 is a term because 87^3 = (13^3 + 54^3 + 122^3) / 3.
457 is a term because 457^3 = (226^3 + 379^3 + 604^3) / 3.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023042, A024975.