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powerful n.  and  wasteful n.

First numbers that belong to both sets:

4, 8, 9, 36, 72, 100, 108, 144, 196, 200, 216, 225, 288, 324, 392, 400, 432, 441, 484, 500, 576, 648, 675, 676, 784, 800, 864, 900, 968, 972, 1089, 1156, 1352, 1444, 1521, 1764, 1800, 1936, 2116, 2312, 2601, 2700, 2704, 2888, 3025, 3249, 3267, 3364, 3528, 3600, 3844, 3872, 4225, 4232, 4356, 4500, 4563, 4624, 4761, 4900, 5292, 5324, 5400, 5408, 5476, 5776, 5929, 6084, 6724, 6728, 7056, 7200, 7225, 7396, 7569, 7688, 7744, 7803, 8100, 8281, 8464, 8649, 8712, 8788, 8836, 9000, 9025, 9216, 9248, 9747, 9800, 9801, 10404, 10584, 10800, 11025, 12100, 12168, 12348, 12996, 13068, 13500, 14112, 14400, 15876, 16200, 16900, 17424, 18000, 18252, 19044, 19600, 20449, 20808, 21168, 21600, 22500, 23716, 24200, 24300, 24336, 24500, 24696, 25992, 26136, 27000, 27225, 28224, 28800, 28900, 30276, 31212, 31752, 32400, 33075, 33124, 33800, 34300, 34596, 34848, 34969, 36000, 36100, 36504, 37044, 38025, 38088, 38988, 39200, 39204, 40500, 40804, 41616, 42336, 42436, 43200, 43681, 44100, 45000, 45796, 47432, 47524, 47628, 47916, 48400, 48600, 48672, 48841, 49000, 49284, 49392, 51076, 51984, 52272, 52900, 53361, 54000, 54756, 55125, 56448, 56644, 57132, 57600, 57800, 60500, 60516, 60552, 61009, 62424, 63504, 64009, 64516, 64800, 65025, 66248, 66564, 67500, 67600, 68600, 68644, 69192, 69696, 70756, 72000, 72200, 72900, 73008, 74088, 74529, 75076, 76176, 77175, 77284, 77976, 78400, 78408, 79092, 79524, 81000, 81225, 81608, 81675, 81796, 83232, 84100, 84500, 84672, 84872, 86400, 86436, 88200, 88804, 89401, 90000, 90828, 91204, 91592, 91809, 93636, 94864, 95048, 95256, 95481, 95832, 96100, 96800, 97200, 97344, 98000, 98568, 98596, 98784, 99225, 101124, 103684, 103788, 103968, 104544, 105800, 108900, 109512, 113288, 114075, 114264, 115600, 116964, 117612, 119025, 121000, 121032, 121104, 124848, 125316, 127449, 132300, 132496, 133100, 133128, 133956, 135200.

Some larger examples :