A066890 Cubes that are the sum of three distinct positive cubes.

216, 729, 1728, 5832, 6859, 8000, 13824, 15625, 19683, 21952, 24389, 27000, 46656, 54872, 64000, 68921, 74088, 85184, 91125, 97336, 110592, 125000, 148877, 157464, 175616, 185193, 195112, 216000, 250047, 287496, 300763, 328509, 343000, 357911, 373248, 421875

Offset: 1

Author

Harvey P. Dale, Jan 22 2002

Keywords

• nonn

Examples

			729 is included because it is 9^3 and 1^3 + 6^3 + 8^3 = 729.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), pp. 130, 147.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Programs

Mathematica

maxCube = (m = 67)^3; Reap[ Do[ bmax = (maxCube - a^3)^(1/3) // Ceiling; Do[ cmax = (maxCube - b^3)^(1/3) // Ceiling; Do[ n = a^3 + b^3 + c^3; If[n <= maxCube, If[ IntegerQ[n^(1/3)], Sow[n]]], {c, b, cmax}], {b, a, bmax}], {a, 1, (maxCube - 2)^(1/3) // Ceiling}]][[2, 1]] // Flatten // Union (* Jean-François Alcover, Mar 07 2013 *)

Formula

a(n) = (A023042(n))^3. - Christian N. K. Anderson, Aug 10 2014

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 06 2012