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

%I A078129 #27 Feb 16 2025 08:32:48
%S A078129 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,
%T A078129 30,31,33,34,36,37,38,39,41,42,44,45,46,47,49,50,52,53,55,57,58,60,61,
%U A078129 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
%N A078129 Numbers which cannot be written as sum of cubes > 1.
%C A078129 A078128(a(n))=0.
%C A078129 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
%C A078129 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
%H A078129 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>.
%H A078129 <a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>
%e A078129 181 is not in the list since 181 = 7*2^3 + 5^3.
%t A078129 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]];
%t A078129 Complement[Range[Max[A078131]], A078131] (* _Jean-François Alcover_, Aug 04 2018 *)
%Y A078129 Cf. A000578, A078131, A078133, A078130, A078135.
%K A078129 nonn,fini,full
%O A078129 1,2
%A A078129 _Reinhard Zumkeller_, Nov 19 2002
%E A078129 Sequence completed by _Franklin T. Adams-Watters_, Apr 21 2006
%E A078129 Edited by _R. J. Mathar_ and _N. J. A. Sloane_, Jul 06 2010