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.

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, 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, 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

Offset

1,42

Links

Table of n, a(n) for n=1..105.

Example

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.

Crossrefs

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

Sequence in context: A257469 A275947 A337976 * A309367 A347709 A122179

Adjacent sequences: A125002 A125003 A125004 * A125006 A125007 A125008

Keyword

easy,nonn

Author

Jens Voß, Nov 15 2006

Status

approved