The ceiling is breaking

Algebra Level 5

n2+n3+n6=n+1 \large \left \lceil \dfrac n2 \right \rceil + \left \lceil \dfrac n3 \right \rceil + \left \lceil \dfrac n6 \right \rceil = n+1

How many positive integers 1n1001\leq n \leq100 satisfy the equation above?

Notation: \lceil \cdot \rceil denotes the ceiling function.


Inspiration.

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