A029780 Every digit that appears in n also appears at least once in both n^2 and n^3.

0, 1, 5, 6, 10, 11, 25, 50, 55, 60, 64, 66, 76, 99, 100, 101, 110, 111, 112, 115, 116, 125, 225, 250, 275, 288, 323, 376, 405, 499, 500, 501, 502, 525, 550, 555, 600, 602, 625, 640, 642, 644, 660, 666, 676, 724, 726, 733, 755, 760, 776, 777, 833