A078129 Numbers which cannot be written as sum of cubes > 1.

1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 93, 95, 98, 100, 101, 103, 106, 109, 111, 114, 117, 119, 122, 127, 130, 138, 146, 154

Offset: 1

Author

Reinhard Zumkeller, Nov 19 2002

Keywords

• nonn
• fini
• full

Comments

A078128(a(n))=0.

The sequence is finite because every number greater than 181 can be represented using just 8 and 27. - Franklin T. Adams-Watters, Apr 21 2006

More generally, the numbers which are not the sum of k-th powers larger than 1 are exactly those in [1, 6^k - 3^k - 2^k] but not of the form 2^k*a + 3^k*b + 5^k*c with a,b,c nonnegative. This relies on the following fact applied to m=2^k and n=3^k: if m and n are relatively prime, then the largest number which is not a linear combination of m and n with positive integer coefficients is mn - m - n. - Benoit Jubin, Jun 29 2010

Examples

			181 is not in the list since 181 = 7*2^3 + 5^3.
		

Links

• Eric Weisstein's World of Mathematics, Cubic Number.
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000578, A078131, A078133, A078130, A078135.

Programs

Mathematica

terms = 83; A078131 = (Exponent[#, x]& /@ List @@ Normal[1/Product[1-x^j^3, {j, 2, Ceiling[(3 terms)^(1/3)]}] + O[x]^(3 terms)])[[2 ;; terms+1]];
Complement[Range[Max[A078131]], A078131] (* Jean-François Alcover, Aug 04 2018 *)

Extensions

Sequence completed by Franklin T. Adams-Watters, Apr 21 2006

Edited by R. J. Mathar and N. J. A. Sloane, Jul 06 2010