A number theory problem by D G

Number Theory Level pending

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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