Search a number
perfect power  and  wasteful n.

First numbers that belong to both sets:

4, 8, 9, 36, 100, 144, 196, 216, 225, 324, 400, 441, 484, 576, 676, 784, 900, 1089, 1156, 1444, 1521, 1764, 1936, 2116, 2601, 2704, 3025, 3249, 3364, 3600, 3844, 4225, 4356, 4624, 4761, 4900, 5476, 5776, 5929, 6084, 6724, 7056, 7225, 7396, 7569, 7744, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9801, 10404, 11025, 12100, 12996, 14400, 15876, 16900, 17424, 19044, 19600, 20449, 22500, 23716, 24336, 27000, 27225, 28224, 28900, 30276, 32400, 33124, 34596, 34969, 36100, 38025, 39204, 40804, 41616, 42436, 43681, 44100, 45796, 47524, 48400, 48841, 49284, 51076, 51984, 52900, 53361, 54756, 56644, 57600, 60516, 61009, 63504, 64009, 64516, 65025, 66564, 67600, 68644, 69696, 70756, 72900, 74088, 74529, 75076, 76176, 77284, 78400, 79524, 81225, 81796, 84100, 86436, 88804, 89401, 90000, 91204, 91809, 93636, 94864, 95481, 96100, 97344, 98596, 99225, 101124, 103684, 108900, 115600, 116964, 119025, 121104, 125316, 127449, 132496, 133956, 136900, 138384, 139876, 144400, 148225, 152100, 156816, 159201, 161604, 164836, 166464, 168100, 171396, 174724, 176400, 181476, 184041, 184900, 188356, 189225, 191844, 193600, 195364, 197136, 207025, 207936, 211600, 213444, 216225, 219024, 220900, 224676, 226576, 230400, 233289, 242064, 244036, 245025, 248004, 256036, 260100, 266256, 268324, 270400, 272484, 278784, 280900, 283024, 285156, 287496, 298116, 302500, 304704, 308025, 311364, 314721, 318096, 324900, 327184, 329476, 336400, 338724, 342225, 348100, 352836, 354025, 357604, 362404, 367236, 370881, 372100, 374544, 378225, 379456, 381924, 384400, 389376, 393129, 396900, 404496, 407044, 412164, 414736, 416025, 417316, 422500, 423801, 427716, 432964, 435600, 439569, 442225, 443556, 448900, 451584, 459684, 462400, 465124, 467856, 474552, 476100, 480249, 484416, 492804, 497025, 501264, 504100, 509796, 511225, 527076, 529984, 532900, 535824, 544644, 547600, 549081, 550564, 553536, 559504, 568516, 576081, 577600, 580644, 585225, 592900, 599076, 603729, 608400, 611524, 617796, 624100, 627264, 632025, 636804, 646416, 648025, 649636.

Some larger examples :