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frugal n.  and  odious n.

First numbers that belong to both sets:

128, 256, 512, 625, 1024, 1029, 1250, 1681, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2401, 3481, 3584, 4096, 4374, 4489, 4802, 5041, 6241, 7921, 8192, 9409, 10000, 10082, 10112, 10201, 10368, 10443, 10496, 10609, 10625, 10752, 10935, 11045, 11125, 11163, 11767, 11907, 12005, 12032, 12167, 12416, 12482, 12544, 12691, 12769, 12800, 13125, 14063, 14336, 14375, 14641, 14749, 15104, 15379, 15463, 15616, 15625, 15842, 15872, 16121, 16129, 16384, 16767, 16807, 17152, 17161, 17253, 17496, 17739, 17920, 18225, 18605, 18688, 18818, 18944, 19208, 19321, 19663, 20000, 20224, 20577, 20736, 20923, 20992, 21141, 21609, 21627, 21870, 21875, 22201, 22599, 23571, 23763, 24010, 24057, 24064, 24334, 24367, 24389, 24649, 24832, 25039, 25088, 25515, 26047, 26411, 26569, 26973, 27097, 27889, 28125, 28561, 28672, 29282, 29375, 29889, 29929, 30208, 30625, 31213, 31232, 31250, 32041, 32761, 32768, 33271, 33614, 34263, 34304, 34375, 34445, 34992, 35287, 35721, 36015, 36875, 37249, 37303, 37376, 38125, 38416, 38809, 39605, 40000, 40448, 40625, 41472, 42875, 43011, 43687, 43750, 43923, 48223, 48778, 48843, 49375, 49664, 49729, 50301, 50421, 50625, 51529, 51759, 52441, 53125, 54675, 55447, 57121, 57122, 57344, 59049, 59375, 60625, 62500, 63001, 64881, 65536, 65625, 66049, 67228, 67797, 69169, 69984, 70713, 71875, 73167, 73205, 73441, 76832, 79507, 80000, 80089, 80919, 84375, 85293, 89667, 90625, 91125, 94041, 94249, 96875, 97969, 98441, 100352, 100499, 100602, 100736, 100842, 101120, 101125, 101185, 101250, 101375, 101632, 101875, 101888, 102400, 102541, 102625, 102789, 102885, 102973, 103058, 103125, 103173, 103243, 103375, 103518, 103552, 103680, 103936, 104615, 104704, 104733, 104882, 104960, 105125, 105149, 105344, 105625, 105856, 105861, 106112, 106240, 106250, 106496, 106625, 106673, 107125, 107163, 107264, 107359, 107375, 107584, 107648, 107653, 107776, 107875, 107911, 108032, 108151, 108241, 109056, 109107, 109350, 109443, 109503, 109625, 109760, 109952, 110336, 110375, 110848, 110875.

Some larger examples :