

A078129


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


6



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
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OFFSET

1,2


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. AdamsWatters, Apr 21 2006
More generally, the numbers which are not the sum of kth 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


LINKS

Table of n, a(n) for n=1..83.
Eric Weisstein's World of Mathematics, Cubic Number.
Index entries for sequences related to sums of cubes


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A000578, A078131, A078133, A078130, A078135.
Sequence in context: A004709 A048107 A342521 * A325368 A325251 A330977
Adjacent sequences: A078126 A078127 A078128 * A078130 A078131 A078132


KEYWORD

nonn,fini,full


AUTHOR

Reinhard Zumkeller, Nov 19 2002


EXTENSIONS

Sequence completed by Franklin T. AdamsWatters, Apr 21 2006
Edited by R. J. Mathar and N. J. A. Sloane, Jul 06 2010


STATUS

approved



