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A048929 Numbers that are the sum of 6 positive cubes in exactly 1 way.

%I A048929 #22 Feb 16 2025 08:32:40
%S A048929 6,13,20,27,32,34,39,41,46,48,53,58,60,65,67,69,72,76,79,83,84,86,90,
%T A048929 91,95,97,98,102,104,105,109,110,116,117,121,123,124,128,130,132,135,
%U A048929 136,137,139,142,143,144,146,147,151,153,154,156,160,161,162,163,170
%N A048929 Numbers that are the sum of 6 positive cubes in exactly 1 way.
%C A048929 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 A048929 T. D. Noe, <a href="/A048929/b048929.txt">Table of n, a(n) for n=1..841</a>
%H A048929 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>.
%t A048929 Select[ Range[200], Length[ Select[ PowersRepresentations[#, 6, 3], And @@ (Positive /@ #) &]] == 1 &] (* _Jean-François Alcover_, Oct 25 2012 *)
%o A048929 (Python)
%o A048929 from collections import Counter
%o A048929 from itertools import combinations_with_replacement as multi_combs
%o A048929 def aupto(lim):
%o A048929   c = filter(lambda x: x<=lim, (i**3 for i in range(1, int(lim**(1/3))+2)))
%o A048929   s = filter(lambda x: x<=lim, (sum(mc) for mc in multi_combs(c, 6)))
%o A048929   counts = Counter(s)
%o A048929   return sorted(k for k in counts if counts[k]==1)
%o A048929 print(aupto(20000)) # _Michael S. Branicky_, Jun 13 2021
%Y A048929 Cf. A003329, A048930, A048931.
%Y A048929 Cf. A057907 (numbers not the sum of six positive cubes)
%K A048929 nonn,fini
%O A048929 1,1
%A A048929 _Eric W. Weisstein_