# Floor & floor

How many integers, between 1 and 2016 inclusive, can be represented in the form of $\lfloor x \lfloor x \rfloor \rfloor$ for some positive $x$?

 Notation: $\lfloor \cdot \rfloor$ denotes the floor function.

Bonus: What if it's $\lfloor x \lfloor x \lfloor x \rfloor \rfloor \rfloor$ instead of $\lfloor x \lfloor x \rfloor \rfloor$?

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