A problem by Josh Rowley

Level pending

\( \sum_{i=1}^{2014} a_{i} = 100 \), where \( a_{k} \in \mathbb{R} , a_{k} \) > \( {0} \) \(\forall k \). What is the minimum value of \( \lfloor 10000 \sum_{i=1}^{2014} \dfrac{a_{i}^2}{i} \rfloor \)?

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