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 A125005 Numbers of orders of nontrivial positive magic-squares with magic sum n. A nontrivial positive magic square is a k-by-k array of consecutive positive integers (not necessarily including 1) such that all rows, all columns and the two diagonals each add up to the same constant (the "magic sum"), with the additional restriction that k (the "order") is greater than 1. 13

%I

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,

%T 0,1,0,1,1,0,0,2,0,0,1,1,0,1,0,1,1,0,0,2,0,0,1,1,0,1,0,1,1,0,1,2,0,0,

%U 1,2,0,1,0,1,2,0,0,2,0,1,1,1,0,1,1,1,1,0,0,3,0,0,1,1,1,1,0,1,1,1,0,2,0,0,2

%N Numbers of orders of nontrivial positive magic-squares with magic sum n. A nontrivial positive magic square is a k-by-k array of consecutive positive integers (not necessarily including 1) such that all rows, all columns and the two diagonals each add up to the same constant (the "magic sum"), with the additional restriction that k (the "order") is greater than 1.

%e A125005(15)=1 because there is exactly one order k > 1 (namely k = 3) such that there exists a magic square of order k having the magic sum 15. By adding 1 to each table cell of one such magic square, a magic square with magic sum 18 is obtained, hence A125005(18) = 1 as well.

%Y Cf. A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

%K easy,nonn

%O 1,42

%A _Jens Voß_, Nov 15 2006

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Last modified April 11 22:31 EDT 2021. Contains 342895 sequences. (Running on oeis4.)