Is it a 4x4 Magic Square?

Logic Level 5

Find the sum of all possible integral values of nn where n2n \geq 2, such that the numbers 11 to 1616 can be written each in one square of a squared 4×44 \times 4 paper (no repetitions allowed), such that each of the 88 sums of the numbers in rows and columns is a multiple of nn, and all of these 88 multiples of n n are different from one other?

Inspiration.

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