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interprime n.  and  perfect power

First numbers that belong to both sets:

4, 9, 64, 81, 144, 225, 324, 441, 625, 1089, 1681, 1728, 2601, 3600, 4096, 5184, 6084, 8464, 12544, 13689, 16641, 17576, 19044, 19600, 21952, 25281, 27225, 28224, 29584, 36864, 38025, 39204, 45369, 46656, 47524, 51984, 56169, 74529, 87025, 88804, 91809, 92416, 95481, 103684, 106929, 108900, 110592, 114244, 116964, 126736, 129600, 133956, 149769, 154449, 166464, 173056, 184041, 186624, 194481, 195112, 199809, 207936, 216225, 223729, 242064, 258064, 260100, 263169, 278784, 285156, 287496, 306916, 313600, 314432, 314721, 321489, 328329, 336400, 338724, 345744, 370881, 391876, 393129, 405224, 412164, 425104, 443556, 446224, 459684, 474552, 481636, 501264, 518400, 527076, 529984, 540225, 541696, 553536, 556516, 571536, 592900, 617796, 646416, 649636, 651249, 669124, 749956, 753424, 795664, 804609, 822649, 898704, 931225, 950625, 970225, 992016, 1014049, 1028196, 1061208, 1069156, 1071225, 1108809, 1121481, 1147041, 1170724, 1179396, 1191016, 1214404, 1234321, 1238769, 1276900, 1285956, 1306449, 1324801, 1343281, 1375929, 1404928, 1430416, 1440000, 1468944, 1483524, 1512900, 1520289, 1527696, 1535121, 1557504, 1572516, 1577536, 1597696, 1601613, 1602756, 1610361, 1677025, 1713481, 1718721, 1758276, 1779556, 1782225, 1798281, 1806336, 1898884, 1906624, 2000376, 2010724, 2047761, 2125764, 2143296, 2146225, 2146689, 2172676, 2178576, 2197000, 2250000, 2286144, 2316484, 2411809, 2414916, 2433600, 2442969, 2449225, 2518569, 2588881, 2595321, 2614689, 2637376, 2650384, 2692881, 2709316, 2729104, 2778889, 2805625, 3017169, 3059001, 3175524, 3189796, 3200000, 3241792, 3243601, 3261636, 3283344, 3337929, 3363556, 3381921, 3511808, 3511876, 3560769, 3579664, 3610000, 3617604, 3636649, 3655744, 3667225, 3701776, 3721041, 3736489, 3775249, 3814209, 3912484, 3936256, 3992004, 4145296, 4161600, 4235364, 4272489, 4276624, 4318084, 4359744, 4376464, 4410000, 4511376, 4528384, 4549689, 4609609, 4730625, 4743684, 4774225, 4796100, 4888521, 4913000, 4937284, 4990756, 5035536, 5053504, 5058001, 5125696, 5212089, 5268024, 5271616, 5280804, 5391684, 5400976, 5433561, 5517801, 5527201, 5550736, 5588496, 5597956, 5607424, 5616900, 5890329, 5973136, 5978025, 6115729, 6130576, 6180196, 6190144, 6229504, 6240004, 6280036, 6300100, 6405961, 6471936, 6584356, 6702921, 6751269, 6770404, 6843456, 6859000, 6937956, 7064964.

Some larger examples :