A358445 -id:A358445 - cp's OEIS frontend

A271580 Magic sums of 4 X 4 magic squares composed of squares.

2823, 3230, 4350, 4590, 6462, 7150, 7735, 7905, 8515, 9230, 9775, 9945, 10625, 11220, 11292, 11310, 11985, 12155, 12675, 12750, 12920, 13050, 13390, 13775, 14355, 14705, 14825, 15275, 15300, 15950, 16150, 16250, 16830, 17300, 17316, 17400, 18315, 18360

Offset: 1

Arkadiusz Wesolowski, Apr 10 2016

nonn

The magic sum of Allan W. Johnson, Jr.'s 4 X 4 magic square of squares (A359383) is 93025. - Robert C. Lyons, Dec 30 2022

The magic sum of Euler's magic square (A358445) is 8515. - Michel Marcus, Dec 30 2022

			Square with magic constant a(1) = 2823:
  |----|----|----|----|
  | 3^2|  1 |38^2|37^2|
  |----|----|----|----|
  | 2^2|47^2|13^2|21^2|
  |----|----|----|----|
  |43^2|18^2|11^2|23^2|
  |----|----|----|----|
  |31^2|17^2|33^2|22^2|
  |----|----|----|----|
Square with magic constant a(2) = 3230:
  |----|----|----|----|
  |13^2|  1 |42^2|36^2|
  |----|----|----|----|
  | 6^2|48^2|19^2|23^2|
  |----|----|----|----|
  |44^2|22^2| 9^2|27^2|
  |----|----|----|----|
  |33^2|21^2|32^2|26^2|
  |----|----|----|----|

Paul Pierrat, François Thiriet and Paul Zimmermann, Magic square of squares
Index entries for sequences related to magic squares

Cf. A000290, A271579, A271711, A359383, A358445. Subsequence of A271581. Supersequence of A271582.

A364276 A 5 X 5 magic square of squares with the smallest possible magic sum, read by rows.

Original entry on oeis.org

1, 4, 961, 9, 400, 484, 256, 169, 25, 441, 121, 529, 100, 576, 49, 144, 225, 81, 729, 196, 625, 361, 64, 36, 289

Offset: 1

Paolo Xausa, Jul 17 2023

This magic square was discovered by Christian Boyer in 2004. It's composed of the squares of the numbers from 1 to 31, excluding 4, 18, 26, 28, 29 and 30. The magic sum is 1375.

			The magic square is:
  [    1    4  961    9  400 ]
  [  484  256  169   25  441 ]
  [  121  529  100  576   49 ]
  [  144  225   81  729  196 ]
  [  625  361   64   36  289 ]
Or equivalently:
  [  1^2  2^2 31^2  3^2 20^2 ]
  [ 22^2 16^2 13^2  5^2 21^2 ]
  [ 11^2 23^2 10^2 24^2  7^2 ]
  [ 12^2 15^2  9^2 27^2 14^2 ]
  [ 25^2 19^2  8^2  6^2 17^2 ]

Christian Boyer, Some notes on the magic squares of squares problem, The Mathematical Intelligencer 27 (2005), pp. 52-64.
Christian Boyer, First known 4x4 to 7x7 magic squares of squares.
Index entries for sequences related to magic squares

Cf. A272932, A358445, A359383.

cp's OEIS Frontend

A271580 Magic sums of 4 X 4 magic squares composed of squares.

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