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Friedman n.  and  frugal n.

First numbers that belong to both sets:

125, 128, 343, 625, 1024, 1792, 2048, 2187, 3125, 4096, 8192, 10201, 10368, 10935, 11163, 11664, 12167, 12288, 12544, 12769, 13125, 13824, 14641, 15379, 15552, 15625, 16384, 16807, 16875, 17253, 17920, 18225, 18723, 19321, 19683, 20736, 21870, 21875, 21952, 23328, 24367, 24389, 24576, 26244, 26973, 27783, 27889, 28561, 28672, 29282, 29929, 30625, 31250, 31347, 32761, 32768, 32805, 34992, 35721, 37179, 37249, 38416, 38637, 39366, 41472, 42875, 44375, 45927, 46656, 46875, 49152, 51759, 52488, 59049, 59375, 65536, 67228, 69984, 76832, 78125, 78732, 81920, 83521, 84375, 85293, 91125, 91854, 93312, 98304, 98415, 102487, 102541, 102912, 103680, 103823, 104375, 104976, 105625, 107163, 107584, 107649, 107653, 108135, 108241, 108864, 109350, 109375, 111537, 112509, 114242, 114244, 114688, 115248, 115625, 116640, 117128, 117369, 117625, 117632, 117649, 118336, 119375, 121203, 121945, 123245, 124375, 124416, 124609, 124659, 125000, 125056, 126025, 126736, 126846, 127253, 127488, 127575, 127744, 128512, 129654, 130321, 131072, 131250, 131584, 131769, 132608, 132651, 133125, 133225, 133563, 134375, 134456, 134689, 135247, 135424, 135625, 136161, 136857, 137216, 137641, 137728, 137781, 137842, 138753, 139129, 139239, 139258, 139264, 139968, 140608, 140625, 141376, 141659, 142805, 143648, 146334, 146410, 146461, 146689, 146875, 147456, 147501, 148862, 148955, 148992, 151263, 151875, 153664, 155277, 155520, 155648, 156249, 156250, 156271, 157464, 157922, 158193, 159375, 161051, 163296, 163840, 164025, 165625, 165888, 166375, 167042, 167281, 168070, 168399, 168750, 169216, 170343, 170471, 170569, 171366, 171875, 172543, 172773, 175232, 175273, 175616, 176435, 177147, 177241, 177674, 178929, 179334, 180625, 180736, 182250, 182272, 183347, 184375, 184832, 184877, 185193, 186245, 186624, 188416, 190269, 192721, 194481, 194672, 195112, 196249, 196587, 196608, 196830, 196875, 198025, 201433, 203391, 204800, 205379, 206486, 208537, 209952, 210125, 210681, 214326, 214369, 214375, 215168, 215296, 216513, 217083, 217728, 218489, 218491, 218750, 219961, 221184, 221875, 222784, 223074, 225625, 225694, 226981, 227529, 228488.

Some larger examples :