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evil n.  and  frugal n.

First numbers that belong to both sets:

125, 243, 343, 729, 1215, 1280, 1331, 1369, 1458, 1536, 1701, 2209, 2560, 2809, 3125, 3645, 3721, 4375, 4913, 5103, 5329, 6250, 6561, 6859, 6889, 7203, 9375, 10125, 10206, 10240, 10375, 10449, 10624, 10633, 10658, 10976, 10985, 11008, 11392, 11421, 11449, 11664, 11776, 11875, 11881, 12125, 12288, 12393, 12500, 12879, 12943, 13122, 13467, 13568, 13718, 13778, 13824, 13851, 14045, 14337, 14406, 14739, 14823, 14848, 15123, 15309, 15552, 15987, 16000, 16281, 16875, 17405, 18125, 18176, 18179, 18723, 18750, 18769, 19197, 19375, 19683, 20169, 20237, 20480, 20667, 21248, 21952, 22016, 22445, 22784, 22801, 22981, 23125, 23328, 24353, 24565, 24576, 25000, 25205, 25625, 26244, 26645, 26875, 27136, 27783, 28227, 28431, 28469, 29791, 30375, 30527, 30618, 31104, 31205, 31347, 31423, 32000, 32805, 33125, 34295, 34391, 36352, 36481, 36501, 37179, 38637, 39366, 39601, 40817, 40960, 41553, 41875, 42496, 43904, 44375, 44469, 44521, 45568, 45619, 45625, 45927, 46656, 46875, 47045, 48013, 49152, 50000, 50653, 51875, 52488, 53217, 54289, 55223, 55625, 57591, 58081, 59582, 60025, 60507, 60835, 62208, 63423, 64000, 64827, 65610, 65863, 68921, 69629, 72171, 72361, 74431, 76545, 76729, 78125, 78732, 78961, 81920, 83349, 83521, 84035, 85169, 85683, 85849, 87808, 88837, 89373, 91854, 93312, 93750, 96721, 98304, 98415, 100000, 100359, 100467, 100489, 100625, 100845, 100864, 100949, 101251, 101306, 101331, 101817, 102016, 102303, 102487, 102656, 102875, 102912, 103247, 103259, 103335, 103499, 103625, 103750, 103761, 103808, 103823, 103933, 104375, 104875, 104976, 105088, 105219, 105301, 105705, 105728, 106097, 106434, 106677, 107392, 107649, 107811, 107909, 108045, 108125, 108135, 108544, 108578, 108621, 108731, 108864, 109091, 109184, 109312, 109375, 109561, 109696, 109744, 110079, 110080, 110125, 110224, 110446, 110464, 110473, 110592, 110625, 110889, 111005, 111051, 111250, 111537, 111747, 111875, 112128, 112768, 112995, 113481, 113536, 113569, 113967, 114375, 114905, 114944, 115169, 115182, 115248, 115943.

Some larger examples :