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economical n.  and  frugal n.

First numbers that belong to both sets:

125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2560, 2809, 3125, 3481, 3584, 3645, 3721, 4096, 4374, 4375, 4489, 4802, 4913, 5041, 5103, 5329, 6241, 6250, 6561, 6859, 6889, 7203, 7921, 8192, 9375, 9409, 10000, 10082, 10112, 10125, 10201, 10206, 10240, 10368, 10375, 10443, 10449, 10496, 10609, 10624, 10625, 10633, 10658, 10752, 10935, 10976, 10985, 11008, 11045, 11125, 11163, 11392, 11421, 11449, 11664, 11767, 11776, 11875, 11881, 11907, 12005, 12032, 12125, 12167, 12288, 12393, 12416, 12482, 12500, 12544, 12691, 12769, 12800, 12879, 12943, 13122, 13125, 13467, 13568, 13718, 13778, 13824, 13851, 14045, 14063, 14336, 14337, 14375, 14406, 14641, 14739, 14749, 14823, 14848, 15104, 15123, 15309, 15379, 15463, 15552, 15616, 15625, 15842, 15872, 15987, 16000, 16121, 16129, 16281, 16384, 16767, 16807, 16875, 17152, 17161, 17253, 17405, 17496, 17739, 17920, 18125, 18176, 18179, 18225, 18605, 18688, 18723, 18750, 18769, 18818, 18944, 19197, 19208, 19321, 19375, 19663, 19683, 20000, 20169, 20224, 20237, 20480, 20577, 20667, 20736, 20923, 20992, 21141, 21248, 21609, 21627, 21870, 21875, 21952, 22016, 22201, 22445, 22599, 22784, 22801, 22981, 23125, 23328, 23571, 23763, 24010, 24057, 24064, 24334, 24353, 24367, 24389, 24565, 24576, 24649, 24832, 25000, 25039, 25088, 25205, 25515, 25625, 26047, 26244, 26411, 26569, 26645, 26875, 26973, 27097, 27136, 27783, 27889, 28125, 28227, 28431, 28469, 28561, 28672, 29282, 29375, 29791, 29889, 29929, 30208, 30375, 30527, 30618, 30625, 31104, 31205, 31213, 31232, 31250, 31347, 31423, 32000, 32041, 32761, 32768, 32805, 33125, 33271, 33614, 34263, 34295, 34304, 34375, 34391, 34445, 34992, 35287, 35721, 36015, 36352, 36481, 36501, 36875, 37179, 37249, 37303, 37376, 38125, 38416, 38637, 38809, 39366, 39601, 39605, 40000, 40448, 40625.

Some larger examples :