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Duffinian n.  and  perfect power

First numbers that belong to both sets:

4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 225, 243, 256, 289, 324, 343, 361, 400, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1600, 1681, 1849, 1936, 2025, 2048, 2116, 2187, 2197, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3125, 3136, 3364, 3481, 3600, 3721, 3844, 4096, 4225, 4356, 4489, 4624, 4761, 4913, 5041, 5184, 5329, 5476, 5625, 5776, 6241, 6400, 6561, 6724, 6859, 6889, 7225, 7396, 7569, 7744, 7921, 8100, 8192, 8281, 8464, 8836, 9025, 9216, 9261, 9409, 10000, 10201, 10404, 10609, 10816, 11236, 11449, 11664, 11881, 12100, 12167, 12769, 13225, 13456, 13924, 14161, 14400, 14641, 14884, 15129, 15625, 16129, 16384, 16807, 16900, 17161, 17424, 17956, 18225, 18496, 18769, 19044, 19321, 19600, 19683, 19881, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 22201, 22500, 22801, 23104, 23409, 24389, 24649, 24964, 25281, 25600, 26244, 26569, 26896, 27225, 27556, 27889, 28561, 28900, 29584, 29791, 29929, 30276, 30625, 30976, 31329, 31684, 32041, 32400, 32761, 32768, 33856, 34225, 34969, 35344, 36100, 36481, 36864, 37249, 37636, 38416, 38809, 39601, 40000, 40804, 41209, 41616, 42025, 42436, 42849, 43264, 44521, 44944, 45369, 45796, 46225, 46656, 47089, 47524, 48400, 48841, 49729, 50176, 50625, 50653, 51076, 51529, 52441, 52900, 53824, 54289, 55225, 55696, 57121, 57600, 58081, 58564, 59049, 59319, 59536, 60025, 60516, 61009, 61504, 62001, 62500, 63001, 64009, 64516, 65025, 65536, 66049, 67600, 68121, 68644, 68921, 69169, 69696, 70225, 71289, 71824, 72361, 72900, 73441, 73984, 75076, 76176, 76729, 77284, 78125, 78400, 78961, 79507, 79524, 80089, 80656, 81796, 82369, 82944, 83521, 84100, 85264, 85849, 87025, 87616, 88209, 88804, 89401, 90000, 90601, 91204, 91809, 92416, 93025, 93636, 94249.

Some larger examples :