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frugal n.  and  unprimeable n.

First numbers that belong to both sets:

512, 625, 1715, 1792, 2048, 2560, 10082, 10125, 10206, 10375, 11125, 11664, 11875, 12125, 13778, 14045, 14336, 14375, 15842, 18176, 18605, 18688, 18818, 20000, 20224, 20992, 21952, 23125, 24565, 24832, 25000, 25205, 25515, 27136, 28672, 29375, 30375, 30618, 30625, 31104, 31205, 32768, 33125, 34375, 34445, 34992, 38125, 38416, 40448, 42875, 43904, 45625, 46656, 49375, 50000, 57122, 60835, 67228, 69984, 73205, 80000, 84035, 90625, 91854, 93750, 96875, 98304, 100864, 101120, 101125, 101250, 101306, 101632, 101888, 102625, 103058, 103375, 103625, 103750, 103936, 104375, 104615, 104882, 104960, 105088, 105125, 105625, 105856, 106112, 106250, 106496, 107392, 109056, 109184, 109696, 109760, 109952, 110375, 110464, 111005, 111392, 112000, 112384, 112768, 113408, 113875, 114176, 114242, 114244, 114875, 115625, 116125, 116224, 116608, 116640, 117625, 117632, 118016, 118336, 119072, 119164, 119375, 119936, 120000, 120050, 120320, 120448, 121216, 121670, 121835, 121875, 121984, 122125, 122624, 122875, 123245, 123776, 123875, 124160, 124288, 124375, 124416, 124625, 124928, 126846, 126848, 126875, 126976, 127232, 127616, 128000, 128125, 129654, 130235, 131726, 131875, 132098, 132845, 133225, 133888, 134456, 134656, 135485, 135680, 138752, 139258, 139375, 139445, 140032, 141426, 141568, 142345, 142805, 143125, 143360, 143648, 143750, 144128, 144722, 145152, 145408, 145625, 146334, 146875, 146882, 147712, 147968, 148736, 149645, 150272, 150544, 150625, 151808, 153090, 153125, 153664, 153856, 155648, 156025, 156160, 156875, 156928, 157115, 157464, 157922, 158464, 159375, 159488, 160178, 161312, 161792, 162304, 163296, 163805, 164608, 165625, 165632, 166375, 167168, 167936, 168704, 168750, 170338, 170528, 170586, 171125, 171366, 171955, 173125, 173312, 174848, 174960, 175232, 175616, 176875, 177664, 178746, 179334, 179375, 182250, 182405, 183125, 184064, 184375, 186515, 187648, 188082, 188125, 189952, 190625, 191875, 192080, 192512, 194045, 194048, 195112, 195625, 196096, 196608, 196864, 196882, 198005, 198025, 199168, 199712, 200704, 203125, 203264, 204032, 204085, 205578, 207104, 210625, 210688, 212480, 214326, 214528, 215552, 215625, 218125.

Some larger examples :