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frugal n.  and  pseudoperfect n.

First numbers that belong to both sets:

1280, 1458, 1536, 1792, 2560, 3584, 4374, 10000, 10112, 10206, 10240, 10368, 10496, 10624, 10752, 10976, 11008, 11392, 11664, 11776, 12032, 12288, 12416, 12500, 12544, 12800, 13122, 13568, 13824, 14336, 14406, 14848, 15104, 15552, 15616, 15872, 16000, 17152, 17496, 17920, 18176, 18688, 18750, 18944, 19208, 20000, 20224, 20480, 20736, 20992, 21248, 21870, 21952, 22016, 22784, 23328, 24010, 24064, 24576, 24832, 25000, 25088, 25515, 26244, 27136, 28672, 30208, 30618, 31104, 31232, 32000, 34304, 34992, 36352, 37376, 38416, 39366, 40000, 40448, 40960, 41472, 42496, 43750, 43904, 45568, 46656, 49152, 49664, 50000, 52488, 57344, 62208, 62500, 64000, 65610, 67228, 69984, 76545, 76832, 78732, 80000, 81920, 87808, 91854, 93312, 93750, 98304, 100000, 100352, 100602, 100842, 100864, 101120, 101250, 101632, 101888, 102400, 102656, 102912, 103518, 103680, 103936, 104704, 104960, 104976, 105728, 106240, 106434, 106496, 107264, 107584, 107648, 107776, 108032, 108045, 108544, 108864, 109056, 109312, 109350, 109744, 109760, 110080, 110336, 110592, 110848, 111104, 111392, 112000, 112128, 112384, 113408, 113920, 114176, 114688, 114944, 115182, 115248, 116224, 116640, 116992, 117128, 117248, 118016, 118098, 118125, 118336, 118528, 118784, 119072, 119296, 119552, 120000, 120050, 120064, 120320, 120832, 121014, 121344, 122368, 122472, 122624, 122880, 123008, 123392, 124160, 124416, 124672, 124928, 125000, 125440, 125696, 126846, 126976, 127232, 127488, 127575, 127744, 128000, 128512, 128768, 129654, 129762, 130304, 130816, 131220, 131250, 131584, 131712, 132608, 134456, 134656, 135424, 135594, 135680, 136704, 137216, 137728, 138752, 138915, 139264, 139968, 140000, 140608, 141376, 141426, 141568, 141824, 143360, 143872, 144342, 144896, 145152, 145408, 146334, 146944, 147456, 147968, 148736, 148992, 149504, 150000, 150016, 151040, 151552, 153090, 153664, 154112, 155520, 155648, 156160, 157184, 157216, 157464, 159232, 159488, 160000, 160256, 161792, 161838, 162304, 163296, 163840, 165888, 166698, 167936, 168070, 168448, 168750, 169472, 169984, 170368, 170586, 171366, 171520, 172032, 172544, 173824, 174960, 175000.

Some larger examples :