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A048926 Numbers that are the sum of 5 positive cubes in exactly 1 way.

%I A048926 #19 Feb 16 2025 08:32:40
%S A048926 5,12,19,26,31,33,38,40,45,52,57,59,64,68,71,75,78,82,83,89,90,94,96,
%T A048926 97,101,108,109,115,116,120,127,129,131,134,135,136,138,143,145,146,
%U A048926 150,152,153,155,162,164,169,171,172,176,181,183,188,190,192,194,195
%N A048926 Numbers that are the sum of 5 positive cubes in exactly 1 way.
%C A048926 It appears that this sequence has 11062 terms, the last of which is 1685758. This means that all numbers greater than 1685758 can be written as the sum of five positive cubes in at least two ways. - _T. D. Noe_, Dec 13 2006
%H A048926 T. D. Noe, <a href="/A048926/b048926.txt">Table of n, a(n) for n=1..11062</a>
%H A048926 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number.</a>
%t A048926 Select[ Range[200], Count[ PowersRepresentations[#, 5, 3], r_ /; FreeQ[r, 0]] == 1 &] (* _Jean-François Alcover_, Oct 23 2012 *)
%o A048926 (Python)
%o A048926 from collections import Counter
%o A048926 from itertools import combinations_with_replacement as combs_with_rep
%o A048926 def aupto(lim):
%o A048926   s = filter(lambda x: x<=lim, (i**3 for i in range(1, int(lim**(1/3))+2)))
%o A048926   s2 = filter(lambda x: x<=lim, (sum(c) for c in combs_with_rep(s, 5)))
%o A048926   s2counts = Counter(s2)
%o A048926   return sorted(k for k in s2counts if s2counts[k] == 1)
%o A048926 print(aupto(196)) # _Michael S. Branicky_, May 12 2021
%Y A048926 Cf. A003328, A048927.
%Y A048926 Cf. A057906 (numbers not the sum of five positive cubes)
%K A048926 nonn,fini
%O A048926 1,1
%A A048926 _Eric W. Weisstein_