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frugal n.  and  super-d n.

First numbers that belong to both sets:

1331, 1369, 1681, 1792, 3481, 4489, 6859, 10496, 10609, 10624, 10625, 10633, 10658, 11163, 11881, 12691, 12769, 13824, 16281, 16384, 16767, 17152, 17496, 17920, 18605, 18769, 20169, 22784, 22981, 26569, 28431, 28469, 33271, 33614, 34295, 36481, 38809, 43011, 43904, 44469, 45619, 58081, 60507, 64881, 69169, 72361, 74431, 78125, 80919, 85169, 97969, 101125, 101331, 103058, 103552, 103625, 103808, 104882, 104960, 104976, 105088, 105125, 105149, 105219, 105301, 105344, 105625, 105705, 105728, 105856, 105861, 106097, 106112, 106240, 106250, 106434, 106496, 106625, 106673, 106677, 107125, 107163, 108241, 108731, 109056, 109184, 109312, 109561, 111005, 112627, 113408, 113481, 113569, 113627, 115169, 115591, 116162, 117369, 118803, 119351, 120127, 120875, 122317, 125881, 126976, 127089, 128881, 130181, 130235, 130331, 130816, 131369, 131383, 131769, 134379, 134689, 137781, 138496, 140032, 141824, 144342, 144403, 144669, 145408, 148519, 148877, 149645, 149769, 149931, 153333, 153664, 153819, 155277, 155763, 157464, 158464, 160181, 160381, 161312, 163840, 165669, 165731, 165969, 167281, 168704, 170471, 170569, 171475, 171520, 172225, 173563, 174231, 174960, 176435, 177147, 178119, 179456, 181781, 183347, 187353, 190269, 193027, 193471, 194481, 195223, 198125, 198147, 199781, 200704, 203877, 204849, 206681, 207646, 208537, 208737, 210681, 211631, 212629, 214369, 214569, 214784, 220549, 220672, 223074, 226719, 226981, 227840, 228488, 229375, 229376, 234269, 234981, 236032, 236875, 236883, 236927, 237169, 238869, 240128, 241081, 242757, 247009, 247131, 247151, 247303, 247552, 248576, 249218, 251419, 253783, 253952, 255881, 257645, 259081, 259375, 263169, 266511, 266875, 268119, 271313, 273529, 274432, 281219, 281961, 283318, 283581, 285719, 292681, 293058, 293125, 295245, 297419, 299619, 302526, 302869, 311469, 314531, 316969, 318028, 318719, 320031, 322373, 325069, 331169, 331681, 331776, 332667, 332929, 333053, 333153, 333739, 334084, 334336, 334375, 334562, 334611, 335111, 335872, 336069, 336091, 336140, 336743, 337169, 337408, 337527, 337561, 337657, 337747, 338125, 338432, 338541, 338985, 339968, 340736, 344569, 354631, 356481, 368219, 372287, 372519.

Some larger examples :