A046040 Numbers that are the sum of 6 but no fewer positive cubes.

6, 13, 20, 34, 39, 41, 46, 48, 53, 58, 60, 69, 76, 79, 84, 86, 95, 98, 102, 104, 105, 110, 117, 121, 123, 124, 132, 139, 147, 151, 158, 165, 170, 173, 177, 184, 196, 202, 203, 210, 215, 221, 222, 228, 235, 236, 242, 247, 249, 263, 265, 268, 273, 275, 284, 287

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• fini

Comments

According to the McCurley article, it is conjectured that there are exactly 3922 terms of which the largest is a(3922) = 1290740.

Links

• T. D. Noe, Table of n, a(n) for n=1..3922
• Jan Bohman and Carl-Erik Froberg, Numerical investigation of Waring's problem for cubes, Nordisk Tidskr. Informationsbehandling (BIT) 21 (1981), 118-122.
• K. S. McCurley, An effective seven-cube theorem, J. Number Theory, 19 (1984), 176-183.
• Eric Weisstein's World of Mathematics, Cubic Number.
• Eric Weisstein's World of Mathematics, Waring's Problem.
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A003325, A003072, A003327, A003328, A018890, A018889.

Programs

Mathematica

Select[Range[300], (pr = PowersRepresentations[#, 6, 3]; pr != {} && Count[pr, r_/; (Times @@ r) == 0] == 0)&] (* Jean-François Alcover, Jul 26 2011 *)

Extensions

Corrected by Arlin Anderson (starship1(AT)gmail.com).