Removing Floors

Algebra Level 3

n2+n3+n5=n2+n3+n5 \large \left \lfloor \dfrac n2 \right \rfloor + \left \lfloor \dfrac n3 \right \rfloor + \left \lfloor \dfrac n5 \right \rfloor = \dfrac n2 + \dfrac n3 + \dfrac n5

If nn is a natural number and 1n1001\leqslant n \leqslant 100, then find the number of solutions to the equation above.

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

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