%I #21 Jun 13 2021 11:35:05
%S 6,13,20,27,32,34,39,41,46,48,53,58,60,65,67,69,72,76,79,83,84,86,90,
%T 91,95,97,98,102,104,105,109,110,116,117,121,123,124,128,130,132,135,
%U 136,137,139,142,143,144,146,147,151,153,154,156,160,161,162,163,170
%N Numbers that are the sum of 6 positive cubes in exactly 1 way.
%C It appears that this sequence has 841 terms, the last of which is 19417. This means that all numbers greater than 19417 can be written as the sum of six positive cubes in at least two ways. - _T. D. Noe_, Dec 13 2006
%H T. D. Noe, <a href="/A048929/b048929.txt">Table of n, a(n) for n=1..841</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>.
%t Select[ Range[200], Length[ Select[ PowersRepresentations[#, 6, 3], And @@ (Positive /@ #) &]] == 1 &] (* _Jean-François Alcover_, Oct 25 2012 *)
%o (Python)
%o from collections import Counter
%o from itertools import combinations_with_replacement as multi_combs
%o def aupto(lim):
%o c = filter(lambda x: x<=lim, (i**3 for i in range(1, int(lim**(1/3))+2)))
%o s = filter(lambda x: x<=lim, (sum(mc) for mc in multi_combs(c, 6)))
%o counts = Counter(s)
%o return sorted(k for k in counts if counts[k]==1)
%o print(aupto(20000)) # _Michael S. Branicky_, Jun 13 2021
%Y Cf. A003329, A048930, A048931.
%Y Cf. A057907 (numbers not the sum of six positive cubes)
%K nonn,fini
%O 1,1
%A _Eric W. Weisstein_