A036445 Maximum size of smallest square when a square of side n is tiled with integer sided squares.

1, 1, 2, 1, 3, 1, 4, 3, 5, 2, 6, 2, 7, 5, 8, 2, 9, 3, 10, 7, 11, 4, 12, 5, 13, 9, 14, 5, 15, 5, 16, 11, 17, 7, 18, 7, 19, 13, 20, 6, 21, 7, 22, 15, 23, 7, 24, 9, 25, 17, 26, 8, 27, 11, 28, 19, 29, 9, 30, 10, 31, 21, 32, 13, 33, 10, 34, 23, 35, 11, 36, 11, 37, 25, 38, 14, 39, 13, 40