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frugal n.  and  pernicious n.

First numbers that belong to both sets:

625, 1029, 1250, 1280, 1536, 1681, 1715, 1792, 1849, 1875, 2187, 2197, 2401, 2560, 3481, 3584, 4374, 4489, 4802, 5041, 6241, 9409, 10000, 10082, 10112, 10240, 10368, 10443, 10496, 10609, 10625, 10752, 11045, 11767, 11907, 12032, 12288, 12416, 12482, 12544, 12691, 12769, 12800, 13125, 14063, 14336, 14375, 14641, 15104, 15379, 15616, 15625, 15872, 16121, 16129, 16807, 17152, 17161, 17253, 17496, 17739, 17920, 18225, 18605, 18688, 18818, 18944, 19208, 20000, 20224, 20480, 20577, 20736, 20992, 21141, 21609, 22599, 23571, 24057, 24064, 24367, 24576, 24649, 24832, 25088, 26047, 28125, 28672, 29282, 29375, 29889, 30208, 31213, 31232, 31250, 32761, 33614, 34304, 34375, 34445, 34992, 35721, 36875, 37249, 37376, 38416, 40000, 40448, 40960, 41472, 42875, 43011, 48223, 48843, 49152, 49664, 49729, 50625, 51529, 57344, 59375, 62500, 64881, 65625, 66049, 67228, 67797, 69169, 69984, 70713, 71875, 73167, 73205, 76832, 80000, 81920, 90625, 91125, 94041, 94249, 96875, 97969, 98304, 98441, 100352, 100499, 100736, 101120, 101125, 101185, 101250, 101375, 101632, 101875, 101888, 102400, 102541, 102625, 102789, 103058, 103173, 103375, 103552, 103680, 103936, 104704, 104960, 105149, 105344, 105856, 106112, 106240, 106496, 106625, 106673, 107264, 107359, 107375, 107584, 107648, 107653, 107776, 108032, 108151, 109056, 109503, 109760, 109952, 110336, 110375, 110848, 111104, 111392, 112000, 112023, 112256, 112384, 112509, 112627, 112847, 112999, 113024, 113125, 113375, 113408, 113533, 113627, 113875, 113920, 114005, 114176, 114453, 114688, 116224, 116608, 116992, 117128, 117248, 117625, 117632, 117855, 118125, 118336, 118375, 118528, 118579, 118750, 118803, 118912, 119296, 119313, 119707, 120000, 120125, 120448, 120771, 120832, 121203, 121216, 121375, 121765, 121801, 121835, 121984, 122368, 122451, 123008, 123201, 123392, 123776, 123875, 124288, 124672, 124928, 125000, 125625, 125696, 126603, 126875, 126976, 127575, 127616, 127744, 127939, 128512, 128625, 129762, 129997, 130235, 130891, 131250, 131279, 131369, 131383, 131584, 131712, 131769, 132098, 132608, 132651.

Some larger examples :