A001476 - OEIS

%I #51 Feb 16 2025 08:32:23

%S 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 31,32,33,34,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,

%U 56,57,58,59,60,61,62,63,66,67,68,69,70,71,74,75,76,77,78,79,80

%N Numbers that are not the sum of distinct positive cubes.

%C Complement of A003997.

%C 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 Indices k such that A279329(k) = 0. - _Vaclav Kotesovec_, Sep 22 2017

%H T. D. Noe, <a href="/A001476/b001476.txt">Table of n, a(n) for n = 1..2788</a> (complete sequence)

%H 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 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 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>

%t 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 (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 Cf. A001422, A003997, A279329, A279486.

%K nonn,fini,full

%O 1,1

%A Jeff Adams (jeff.adams(AT)byu.net)

%E Definition clarified by _Jeppe Stig Nielsen_, Jan 27 2015