Crazy Inequalities 2 + 400 followers problem

Algebra Level 5

\[\sum_{k=1}^{400} \frac{k^{3}}{x_{k}^{2}}=1\]

Given the above sum, with positive real numbers \(x_1, x_2, \ldots , x_{400} \).

If the minimum value of \( \displaystyle \sum_{k=1}^{400} x_k \) can be expressed as \(p^{3}\) for a positive real \(p\), input your answer as the greatest integer less than \(400p\).

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