Floor & floor

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

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

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

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