Is it a 4x4 Magic Square?

Logic Level 5

Find the sum of all possible integral values of $$n$$ where $$n \geq 2$$, such that the numbers $$1$$ to $$16$$ can be written each in one square of a squared $$4 \times 4$$ paper (no repetitions allowed), such that each of the $$8$$ sums of the numbers in rows and columns is a multiple of $$n$$, and all of these $$8$$ multiples of $$n$$ are different from one other?

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