Allen William Johnson [1] discovered the following magic square whose entries are all squares.

The following Python code verifies that this is a magic square.

import numpy as np M = np.array( [[ 30**2, 246**2, 172**2, 45**2], [ 93**2, 116**2, 66**2, 258**2], [126**2, 138**2, 237**2, 44**2], [260**2, 3**2, 54**2, 150**2] ]) def verify(M): m, n = M.shape assert(m == n) c = sum(M[0, :]) semimagic = True for i in range(m): semimagic &= sum(M[i,:]) == c semimagic &= sum(M[:,i]) == c d1 = sum(M[i, i ] for i in range(m)) d2 = sum(M[i,-i-1] for i in range(m)) magic = semimagic and (d1 == d2 == c) if magic: return "magic" if semimagic: return "semi-magic" return "not magic" print(verify(M))

## More magic square posts

- Chess themed magic squares: Knight, King
- Planet themed magic squares: Jupiter, Mars
- Language themed magic squares: Spanish, French

[1] Allen William Johnson. Journal of Recreational Mathematics. 22 (1990), 38

Now I’m curious if there exist any magic squares of the form […]^2, and if a hierarchy of squaring is possible.

Here is another (smaller) one, purportedly from Euler (1770):

https://twitter.com/pickover/status/869245576654852096?s=20

Eat your heart out, Matt Parker!

FYI, the discoverer’s name is Allan W. Johnson, Jr.

I added the following sequence to the OEIS: https://oeis.org/A359383

It has a link back to this blog page.