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?

Inspiration.

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