Forum:Idea for a function

So I was watching this video: https://www.youtube.com/watch?v=wymmCdLdPvM

And I came up with this idea. Please keep in mind that I have no real higher math education so I might not be phrasing this right, but this is my best attempt.

For all X which meet the following conditions:


 * There exist integers a, b, and c such that a^3 + b^3 + c^3 = X


 * a, b, and c can include repeats of the same integer (a can equal b can equal c)


 * a, b, and c are all > X

Define FX(n) as the nth smallest positive value of a^3, b^3, or c^3 (whichever is larger) such that a^3 + b^3 + c^3 = X

So for example, using some of the numbers they addressed in the video:

F29(1) = 27

F30(1) = 2,220,422,932^3

So we have a family of functions that grow at quite different rates.

Now define Y as the value of X for which FX(n) grows fastest in where Y <= Z, and Z >= 1

So now we have the function FY(Z), which gives an X. For example, FY(100) would give you the integer X <= 100 for which FX(n) grows fastest.

Now define F(Z, n) = FX(n) where X = FY(Z)

Does this make sense?