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A337366
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Number of representations of A036691(n) as a sum of 3 nonnegative cubes.
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0
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1, 0, 1, 1, 2, 1, 1, 2, 1, 4, 6, 3, 8, 8, 14, 7
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OFFSET
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0,5
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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a(4) = 2 because A036691(4) = 1728 = 12^3 = 6^3 + 8^3 + 10^3.
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MATHEMATICA
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A036691 = Join[{1}, FoldList[Times, Select[Range[20], CompositeQ]]];
Table[Length@ PowersRepresentations[A036691[[n]], 3, 3], {n, 10}] (* Robert Price, Sep 08 2020 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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