# A number theory problem by D G

Let $$f(n)$$ be the number of positive integer solutions $$x < n$$ with $$x^3 \equiv 1 \pmod{n}$$.

Let $$g(k)$$ be the smallest integer $$n$$ such that $$f(n) \geq k$$.

Find $$\displaystyle \sum_{k=1}^{729} g(k)$$.

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