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Achilles n.  and  happy n.

First numbers that belong to both sets:

392, 1125, 1152, 1323, 3200, 3456, 4563, 8748, 10125, 10976, 12348, 14112, 14283, 17672, 18432, 26136, 31212, 32000, 33800, 36504, 39200, 41472, 42592, 44217, 47432, 49000, 52272, 59643, 67712, 69192, 78408, 86528, 91592, 111392, 112500, 115200, 121032, 121203, 121500, 123823, 132300, 134456, 148176, 152352, 154568, 189728, 194688, 202612, 219488, 222264, 223112, 225792, 231125, 231525, 243675, 253125, 254043, 268912, 288463, 291848, 304175, 310472, 313632, 320000, 325125, 338000, 345600, 363312, 364500, 366368, 369800, 381024, 385875, 392000, 401408, 406125, 418176, 435483, 438012, 441800, 456300, 530604, 532512, 544500, 552123, 553352, 555579, 562432, 576583, 583443, 636192, 648675, 653400, 677448, 691488, 707472, 710432, 740772, 744012, 784000, 788768, 793016, 793117, 793800, 798848, 803736, 829939, 855468, 874800, 876488, 878004, 881792, 927472, 953312, 974408, 990125, 1000188, 1012500, 1013888, 1019592, 1025312, 1031048, 1071648, 1077512, 1097600, 1102736, 1112643, 1125000, 1128125, 1152000, 1153852, 1193859, 1202067, 1210104, 1215000, 1216700, 1234800, 1254528, 1275125, 1292832, 1312200, 1318492, 1318688, 1323000, 1333584, 1338248, 1342683, 1344364, 1354752, 1382400, 1411200, 1428300, 1444000, 1449459, 1497375, 1513800, 1516563, 1521000, 1534752, 1541768, 1543275, 1586032, 1597536, 1624500, 1633023, 1634432, 1663488, 1711125, 1714608, 1722368, 1724976, 1737248, 1740500, 1759688, 1767200, 1769472, 1770125, 1788696, 1820232, 1823508, 1835528, 1843200, 1853388, 1854944, 1944392, 1953747, 1975509, 1982907, 2012283, 2027052, 2032128, 2056223, 2064512, 2088968, 2105352, 2130048, 2146592, 2162403, 2203416, 2247264, 2286387, 2298368, 2302128, 2333772, 2350112, 2358792, 2381400, 2381643, 2382032, 2393672, 2426976, 2446227, 2461019, 2478175, 2485125, 2499848, 2613600, 2626632, 2634012, 2667168, 2676429, 2747168, 2747547, 2775368, 2799468, 2869452, 2889608, 2906631, 2910897, 2922507, 2956581, 2956824, 2986568, 3000564, 3012012, 3085128, 3115008, 3121200, 3158028, 3183624, 3205512, 3213675, 3288627, 3316275, 3341637, 3345408, 3361743, 3364000, 3380000, 3383532, 3402675, 3444500, 3456000, 3501153, 3504096, 3527168, 3538188, 3577392, 3594456, 3612672, 3630312, 3631696, 3645000, 3650400, 3698000, 3709888, 3738779, 3756483, 3763584, 3776652, 3786752, 3796875, 3813248, 3864200, 3875508, 3878496, 3920000, 3927007, 3942432, 3954600.

Some larger examples :