The feature that makes this magic square most unusual is another magic square appears within its framework. That demands further inspection.
I found this square on Jollymaths.com
Reducing the numbers of this 9x9 magic square to their Pythagorean root number generates a square of repetitive Luo Shu magic squares. The entire square becomes nine individual 3x3 magic squares.
Notice there are nine consecutive numbers in each grouping with the first nine numbers located in the first row middle column grouping.
The second grouping of consecutive nine numbers, ten thru 18 can be found in the lower right grouping of numbers. The third set of consecutive nine numbers, nineteen thru twenty-seven, can be discovered in the first column middle row group. If each group of nine numbers is assigned its position in a 3x3 grid according to numerical order, then the Luo Shu magic square shows up once again.