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perfect power  and  practical n.

First numbers that belong to both sets:

1, 4, 8, 16, 32, 36, 64, 100, 128, 144, 196, 216, 256, 324, 400, 512, 576, 784, 900, 1000, 1024, 1296, 1600, 1728, 1764, 1936, 2048, 2304, 2500, 2704, 2744, 2916, 3136, 3600, 4096, 4356, 4624, 4900, 5184, 5776, 5832, 6084, 6400, 7056, 7744, 7776, 8000, 8100, 8192, 8464, 9216, 9604, 10000, 10404, 10648, 10816, 11664, 12100, 12544, 12996, 13456, 13824, 14400, 15376, 15876, 16384, 16900, 17424, 17576, 18496, 19044, 19600, 20736, 21952, 22500, 23104, 23716, 24336, 25600, 26244, 27000, 28224, 28900, 30276, 30976, 32400, 32768, 33124, 33856, 34596, 36100, 36864, 38416, 39204, 40000, 41616, 43264, 44100, 46656, 48400, 49284, 50176, 51984, 52900, 53824, 54756, 56644, 57600, 60516, 61504, 62500, 63504, 64000, 65536, 66564, 67600, 69696, 70756, 72900, 73984, 74088, 76176, 78400, 79524, 82944, 84100, 85184, 86436, 87616, 90000, 92416, 93636, 94864, 96100, 97344, 100000, 101124, 102400, 103684, 104976, 107584, 108900, 110592, 112896, 115600, 116964, 118336, 121104, 122500, 123904, 125000, 125316, 129600, 131072, 132496, 133956, 135424, 136900, 138384, 140608, 141376, 142884, 144400, 147456, 152100, 153664, 156816, 157464, 160000, 161604, 164836, 166464, 168100, 171396, 173056, 175616, 176400, 179776, 181476, 184900, 186624, 188356, 191844, 193600, 197136, 200704, 202500, 207936, 211600, 213444, 215296, 216000, 219024, 220900, 222784, 224676, 226576, 230400, 234256, 236196, 238144, 240100, 242064, 246016, 248004, 248832, 250000, 254016, 260100, 262144, 266256, 268324, 270400, 272484, 278784, 279936, 280900, 283024, 285156, 287296, 287496, 291600, 295936, 298116, 302500, 304704, 311364, 313600, 314432, 318096, 322624, 324900, 327184, 329476, 331776, 336400, 341056, 343000, 345744, 348100, 350464, 352836, 360000, 362404, 369664, 372100, 373248, 374544, 379456, 384400, 389376, 396900, 399424, 404496, 409600, 414736, 419904, 422500, 430336, 432964, 435600, 438976, 440896, 443556, 448900, 451584, 456976, 462400, 467856, 470596, 473344, 474552, 476100, 484416, 490000, 492804, 495616, 501264, 504100, 506944.

Some larger examples :