2016 is absolutely awesome 1

Algebra Level 5

20162016k=k;20162016k=k\left\lfloor\dfrac{2016}{\left\lfloor\dfrac{2016}{k}\right\rfloor}\right\rfloor=k\quad;\quad \left\lceil\dfrac{2016}{\left\lceil\dfrac{2016}{k}\right\rceil}\right\rceil=k

An integer 1k20161\le k\le 2016 is called 2016-awesome if it satisfies the equations above.

Find the number of 2016-awesome numbers.


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