This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337366 #14 Sep 11 2020 10:56:58
%S A337366 1,0,1,1,2,1,1,2,1,4,6,3,8,8,14,7
%N A337366 Number of representations of A036691(n) as a sum of 3 nonnegative cubes.
%C A337366 Conjecture I: a(n) = 0 only for n = 1. That is, any product of first n > 1 composite numbers is a sum of at most 3 positive cubes. For example,
%C A337366 A036691(100) = 2563573191821442299652988946477367093137353211904000000000^3 + 21431289850849406740917647451954098598503667204096000000000^3 + 26409890400237152457638095665189553529771293409280000000000^3.
%C A337366 Conjecture II: For any term t >= 1, there are only finitely many values of n such that a(n) = t.
%F A337366 a(n) = A025447(A036691(n)).
%e A337366 a(4) = 2 because A036691(4) = 1728 = 12^3 = 6^3 + 8^3 + 10^3.
%t A337366 A036691 = Join[{1}, FoldList[Times, Select[Range[20], CompositeQ]]];
%t A337366 Table[Length@ PowersRepresentations[A036691[[n]], 3, 3], {n, 10}] (* _Robert Price_, Sep 08 2020 *)
%Y A337366 Cf. A025447, A036691, A226955, A267414.
%K A337366 nonn,more
%O A337366 0,5
%A A337366 _Altug Alkan_, Aug 25 2020