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A001476 Numbers that are not the sum of distinct positive cubes.

%I A001476 #55 Jul 14 2025 06:19:00
%S A001476 2,3,4,5,6,7,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,29,30,
%T A001476 31,32,33,34,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,
%U A001476 56,57,58,59,60,61,62,63,66,67,68,69,70,71,74,75,76,77,78,79,80
%N A001476 Numbers that are not the sum of distinct positive cubes.
%C A001476 Complement of A003997.
%C A001476 There are 85 terms below 100, 793 terms below 1000, but only 2765 terms below 10^4, and only 23 more up to the largest term a(2788)=12758. - _M. F. Hasler_, Feb 25 2012
%C A001476 Indices k such that A279329(k) = 0. - _Vaclav Kotesovec_, Sep 22 2017
%H A001476 T. D. Noe, <a href="/A001476/b001476.txt">Table of n, a(n) for n = 1..2788</a> (complete sequence)
%H A001476 R. E. Dressler and T. Parker, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0327652-1">12,758</a>, Math. Comp. 28 (1974), 313-314.
%H A001476 R. Sprague, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=GDZPPN002380951&amp;IDDOC=24044">Über Zerlegungen in n-te Potenzen mit lauter verschiedenen Grundzahlen</a>, Math. Z. 51, (1948). 466-468.
%H A001476 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%t A001476 Cubes[ n_ ] := Block[ {A, i}, A = {0}; If[ n>0, Do[ A = Union[ A, A + i*i*i ], {i, n} ]; ]; Return[ A ]; ]; Q = Complement[ Table[ i, {i, 1, 12760} ], Cubes[ 23 ] ]
%o A001476 (PARI) select( is_A001476(n,m=n)={m^3>n&&m=sqrtnint(n,3); n!=m^3&&!while(m>1, is_A001476(n-m^3, m--)||return)}, [1..77]) \\ _M. F. Hasler_, Apr 21 2020
%Y A001476 Cf. A001422, A003997, A279329, A279486.
%K A001476 nonn,fini,full
%O A001476 1,1
%A A001476 Jeff Adams (jeff.adams(AT)byu.net)
%E A001476 Definition clarified by _Jeppe Stig Nielsen_, Jan 27 2015