Search a number
deficient n.  and  perfect power

First numbers that belong to both sets:

1, 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 225, 243, 256, 289, 343, 361, 441, 484, 512, 529, 625, 676, 729, 841, 961, 1024, 1089, 1156, 1225, 1331, 1369, 1444, 1521, 1681, 1849, 2025, 2048, 2116, 2187, 2197, 2209, 2401, 2601, 2809, 3025, 3125, 3249, 3364, 3375, 3481, 3721, 3844, 3969, 4096, 4225, 4489, 4761, 4913, 5041, 5329, 5476, 5625, 5929, 6241, 6561, 6724, 6859, 6889, 7225, 7396, 7569, 7921, 8192, 8281, 8649, 8836, 9025, 9261, 9409, 9801, 10201, 10609, 11236, 11449, 11881, 12167, 12321, 12769, 13225, 13689, 13924, 14161, 14641, 14884, 15129, 15625, 16129, 16384, 16641, 16807, 17161, 17689, 17956, 18225, 18769, 19321, 19683, 19881, 20164, 20449, 21025, 21316, 21609, 21904, 22201, 22801, 23409, 24025, 24389, 24649, 24964, 25281, 25921, 26569, 26896, 27225, 27556, 27889, 28561, 29241, 29584, 29791, 29929, 30625, 31329, 31684, 32041, 32761, 32768, 33489, 34225, 34969, 35344, 35721, 35937, 36481, 37249, 37636, 38025, 38809, 39304, 39601, 40401, 40804, 41209, 42025, 42436, 42849, 42875, 43681, 44521, 44944, 45369, 45796, 46225, 47089, 47524, 47961, 48841, 49729, 50625, 50653, 51076, 51529, 52441, 53361, 54289, 54872, 55225, 55696, 56169, 57121, 58081, 58564, 59049, 59319, 59536, 60025, 61009, 62001, 63001, 64009, 64516, 65025, 65536, 66049, 67081, 68121, 68644, 68921, 69169, 70225, 71289, 71824, 72361, 73441, 74529, 75076, 75625, 76729, 77284, 77841, 78125, 78961, 79507, 80089, 80656, 81225, 82369, 83521, 84681, 85264, 85849, 87025, 88209, 88804, 89401, 90601, 91125, 91204, 91809, 93025, 94249, 95481, 96721, 97336, 97969, 98596, 99856, 100489, 101761, 103041, 103823, 104329, 105625, 106276, 106929, 108241, 109561, 110224, 110889, 111556, 112225, 113569, 114244, 114921, 116281, 117649, 119025, 119716, 120409, 121801, 123201, 124609, 126025, 126736, 127449, 128164, 128881, 130321, 131044, 131072, 131769, 132651, 133225.

Some larger examples :