OFFSET
0,5
COMMENTS
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,
A036691(100) = 2563573191821442299652988946477367093137353211904000000000^3 + 21431289850849406740917647451954098598503667204096000000000^3 + 26409890400237152457638095665189553529771293409280000000000^3.
Conjecture II: For any term t >= 1, there are only finitely many values of n such that a(n) = t.
EXAMPLE
a(4) = 2 because A036691(4) = 1728 = 12^3 = 6^3 + 8^3 + 10^3.
MATHEMATICA
A036691 = Join[{1}, FoldList[Times, Select[Range[20], CompositeQ]]];
Table[Length@ PowersRepresentations[A036691[[n]], 3, 3], {n, 10}] (* Robert Price, Sep 08 2020 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Aug 25 2020
STATUS
approved