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interprime n.  and  powerful n.

First numbers that belong to both sets:

4, 9, 64, 72, 81, 108, 144, 225, 288, 324, 432, 441, 625, 675, 1089, 1152, 1681, 1728, 2592, 2601, 3528, 3600, 4096, 4500, 5184, 6084, 7200, 8464, 9000, 10976, 12500, 12544, 13689, 16641, 16875, 17576, 18252, 19044, 19600, 20808, 21600, 21632, 21952, 24200, 25281, 25947, 26912, 27225, 28224, 28800, 29584, 34848, 36864, 37044, 38025, 39204, 41067, 45369, 46656, 47524, 49392, 51984, 56169, 56448, 69192, 74529, 75843, 83232, 83349, 87025, 88804, 90828, 91809, 92416, 95481, 97200, 98568, 103684, 103968, 106929, 108900, 109512, 110592, 114075, 114244, 114264, 116964, 126736, 129600, 133100, 133956, 139968, 146016, 149769, 151263, 154449, 166464, 173056, 180000, 180500, 184041, 186624, 190125, 194481, 195112, 196000, 197568, 199692, 199809, 204800, 207936, 216225, 223729, 242064, 258064, 260100, 260876, 263169, 264600, 273800, 276125, 278784, 285156, 287496, 292032, 299475, 306916, 310472, 313600, 314432, 314721, 316368, 321489, 328329, 336400, 337500, 338724, 345600, 345744, 362952, 370881, 383688, 391876, 393129, 399384, 405224, 412164, 423200, 425104, 431244, 438048, 441000, 443556, 444528, 446224, 449307, 459684, 472392, 474552, 481636, 496125, 501264, 518400, 518616, 527076, 529984, 532512, 540225, 541696, 553536, 556516, 571536, 575532, 591872, 592900, 617796, 646416, 649636, 649800, 651249, 658952, 663552, 666792, 669124, 703125, 708588, 715208, 734472, 749088, 749956, 753424, 795664, 803736, 804609, 808992, 822649, 878004, 892448, 898425, 898704, 931225, 935712, 940896, 950625, 970225, 992016, 995328, 1014049, 1026675, 1028196, 1061208, 1065800, 1069156, 1071225, 1081125, 1108809, 1121481, 1143072, 1147041, 1170724, 1179396, 1190700, 1191016, 1214404, 1218375, 1225000, 1225125, 1234321, 1238769, 1247616, 1254528, 1276900, 1283148, 1285956, 1296000, 1306449, 1312200, 1318707, 1324801, 1342683, 1343281, 1371168, 1375929, 1404488, 1404500, 1404928, 1430416, 1440000, 1468944, 1483524, 1488375, 1512900, 1520289, 1520768, 1521000, 1527696, 1529388, 1535121, 1540125, 1543275, 1557504, 1572516, 1577536, 1597696, 1601613, 1602756, 1610361, 1677025, 1680700, 1685448, 1713481, 1718721, 1724976, 1755675, 1758276, 1779556, 1782225, 1798281, 1799512, 1805000.

Some larger examples :