A221669 3 x 3 magic square containing seven squares, read by rows.

139129, 83521, 319225, 360721, 180625, 529, 42025, 277729, 222121

Offset: 1

Author

Jonathan Sondow, Jan 21 2013

Keywords

• nonn
• tabf
• fini
• full

Comments

Apart from trivial modifications, this is the only known 3 x 3 magic square containing seven squares. No 3 x 3 magic square containing eight or nine squares is known.

The seven integer square roots are A221670.

Examples

			[139129 83521 319225
360721 180625 529
42025 277729 222121]
		

Links

• A. Bremner, On squares of squares, Acta Arith. 88 (1999), 289-297.
• A. Bremner, On squares of squares. II, Acta Arith. 99 (2001), 289-308.
• John P. Robertson, Magic squares of squares, Math. Mag., 69 (1996), 289-293.
• Zentralblatt, Review of "On squares of squares. II" by A. Bremner
• Index entries for sequences related to magic squares

Crossrefs

Cf. A221670, A319589.

Formula

a(1) = 139129 = 373^2, a(2) = 83521 = 289^2, a(3) = 319225 = 565^2, a(5) = 180625 = 425^2, a(6) = 529 = 23^2, a(7) = 42025 = 205^2, a(8) = 277729 = 527^2.