The number M_2(n) | = | 1/n sum_(k = 1)^(n^2) k | = | 1/2 n(n^2 + 1) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first few values are 1, 5, 15, 34, 65, 111, 175, 260, ... (OEIS A006003).
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