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Achilles n.  and  interprime n.

First numbers that belong to both sets:

72, 108, 288, 432, 675, 1152, 2592, 3528, 4500, 7200, 9000, 10976, 12500, 16875, 18252, 20808, 21600, 21632, 24200, 25947, 26912, 28800, 34848, 37044, 41067, 49392, 56448, 69192, 75843, 83232, 83349, 90828, 97200, 98568, 103968, 109512, 114075, 114264, 133100, 139968, 146016, 151263, 180000, 180500, 190125, 196000, 197568, 199692, 204800, 260876, 264600, 273800, 276125, 292032, 299475, 310472, 316368, 337500, 345600, 362952, 383688, 399384, 423200, 431244, 438048, 441000, 444528, 449307, 472392, 496125, 518616, 532512, 575532, 591872, 649800, 658952, 663552, 666792, 703125, 708588, 715208, 734472, 749088, 803736, 808992, 878004, 892448, 898425, 935712, 940896, 995328, 1026675, 1065800, 1081125, 1143072, 1190700, 1218375, 1225000, 1225125, 1247616, 1254528, 1283148, 1296000, 1312200, 1318707, 1342683, 1371168, 1404488, 1404500, 1488375, 1520768, 1521000, 1529388, 1540125, 1543275, 1680700, 1685448, 1724976, 1755675, 1799512, 1805000, 1825200, 1852200, 1867563, 1920800, 1949400, 1960200, 2056752, 2080125, 2105352, 2116800, 2121800, 2144952, 2381400, 2411208, 2446227, 2471625, 2478843, 2536828, 2544768, 2576816, 2598977, 2601000, 2634012, 2661336, 2679075, 2681928, 2696112, 2709504, 2747547, 2758104, 2807136, 2829888, 2847312, 2889608, 2906496, 2947592, 3012012, 3024819, 3121200, 3227287, 3240125, 3267000, 3269808, 3326427, 3359232, 3369608, 3400832, 3402675, 3403125, 3421872, 3444896, 3456000, 3516552, 3538188, 3568572, 3577392, 3612672, 3623432, 3699200, 3721925, 3776652, 3837483, 3841992, 3916125, 4106700, 4173336, 4298427, 4355424, 4371125, 4406832, 4448925, 4464072, 4476032, 4536072, 4572288, 4753125, 4755528, 4762800, 4792608, 4804839, 4808268, 4876875, 4899852, 4929800, 4952651, 5056344, 5100500, 5116364, 5174928, 5250987, 5322672, 5324000, 5329000, 5346675, 5370732, 5394843, 5470524, 5487525, 5848200, 5863212, 5931900, 5953500, 6001128, 6105125, 6143283, 6209288, 6241000, 6242400, 6265800, 6328125, 6390144, 6406452, 6441125, 6482700, 6561000, 6642376, 6771200, 6831243, 6912972, 7159328, 7288556, 7320500, 7390708, 7443468, 7486875, 7698888, 7703584, 7746048, 7751016, 7793352, 8001504, 8128512, 8160800, 8256843, 8300600, 8405000, 8515125, 8652800, 8686112, 8803107, 8820000, 8989056, 9051507, 9077400, 9262208, 9303363, 9430587, 9730125, 9750528, 9800000, 9803592, 9821312, 9834543, 9886500, 9948123, 10074339, 10125000, 10153125, 10171224.

Some larger examples :