Recurring Styles 13 - Game of Inequalities!

Algebra Level 5

$\Large{ a_{n+1} = \dfrac{a_n}{n} + \dfrac{n}{a_n} \quad, \quad a_1 = 1}$

Let the sequence $$\left< a_n \right>$$ be defined as above for all positive integers $$n$$. Evaluate $$\large{\left \lfloor a_{2015} \right \rfloor }$$

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