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⌊2016⌊2016k⌋⌋=k;⌈2016⌈2016k⌉⌉=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⎣⎢⎢⎢⎢⎢⌊k2016⌋2016⎦⎥⎥⎥⎥⎥=k;⎢⎢⎢⎢⎢⎡⌈k2016⌉2016⎥⎥⎥⎥⎥⎤=k
An integer 1≤k≤20161\le k\le 20161≤k≤2016 is called 2016-awesome if it satisfies the equations above.
Find the number of 2016-awesome numbers.
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