Mostperfect magic squares
A magic square is said to be mostperfect, if it contains the consecutive numbers 1, 2, …, n^{2} such that
 any four adjacent integers forming a 2x2subsquare sum to
 any pair of integers distant n/2 along a diagonal sum to
T=n^{2} + 1
 it is a doubleeven magic square, i.e. of order n=4k.
The following magic square with order 4 and 8 are mostperfect.

1  16  17  32  53  60  37  44  63  50  47  34  11  6  27  22  3  14  19  30  55  58  39  42  61  52  45  36  9  8  25  24  12  5  28  21  64  49  48  33  54  59  38  43  2  15  18  31  10  7  26  23  62  51  46  35  56  57  40  41  4  13  20  29 
