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ABA n.  and  happy n.

First numbers that belong to both sets:

32, 192, 338, 392, 1029, 1152, 1215, 3200, 3698, 4418, 7938, 9604, 10125, 11250, 13122, 14112, 15138, 15625, 17672, 18432, 24576, 33800, 36450, 38642, 39200, 41472, 43218, 46875, 47432, 54450, 59049, 65522, 67712, 69192, 71442, 74498, 78408, 86528, 90738, 91592, 101250, 106722, 108578, 111392, 115200, 116162, 121032, 136242, 152352, 154568, 162450, 169362, 174050, 176418, 189728, 190962, 192000, 194688, 208658, 213858, 222264, 223112, 225792, 232562, 257762, 291848, 310472, 313632, 318402, 320000, 341138, 344450, 347778, 351122, 357858, 366368, 369800, 401408, 421362, 432450, 441800, 466578, 499125, 532512, 534578, 553352, 555579, 568178, 590490, 611618, 633938, 636192, 652082, 677448, 691488, 710432, 717602, 761378, 788768, 791282, 793800, 798848, 826898, 876488, 881792, 927522, 974408, 994050, 1011042, 1013888, 1019592, 1025312, 1029000, 1031048, 1071648, 1077512, 1110050, 1125000, 1188882, 1219922, 1254528, 1264050, 1283202, 1292832, 1312200, 1318688, 1338248, 1354658, 1411200, 1462050, 1468898, 1510322, 1513800, 1524258, 1534752, 1538258, 1541768, 1545282, 1562500, 1566450, 1616402, 1634432, 1663488, 1722368, 1737248, 1759688, 1767200, 1820232, 1835528, 1843200, 1856465, 1940450, 1944392, 1956242, 1972098, 1975509, 1996002, 2032128, 2064512, 2088968, 2105352, 2130048, 2146592, 2167362, 2209202, 2228224, 2251442, 2260713, 2285522, 2298368, 2311250, 2350112, 2358792, 2393672, 2415602, 2468642, 2499848, 2522258, 2531250, 2567378, 2626632, 2689120, 2695842, 2738019, 2747168, 2775368, 2798978, 2865618, 2889608, 2910897, 2962178, 2986568, 3011058, 3070242, 3085128, 3115008, 3130002, 3140018, 3170162, 3183624, 3188646, 3205512, 3251250, 3271682, 3278181, 3281922, 3374592, 3380000, 3406050, 3468978, 3479522, 3521858, 3527168, 3543122, 3553778, 3612672, 3645000, 3704642, 3726450, 3759282, 3786752, 3792258, 3796875, 3847538, 3864200, 3920000, 3942432, 3964928, 3981842, 4010112, 4061250, 4141442, 4147200, 4152962, 4164498, 4194304, 4222418, 4234050, 4251528, 4286592, 4321800, 4357152, 4392648, 4452128, 4476032, 4494002, 4536072, 4548128, 4572288, 4578338, 4596512, 4675682, 4743200, 4755528, 4904712, 4942368, 4948658, 4967552, 4980168, 5024450, 5062562, 5126402, 5132808, 5229378, 5294258, 5425218, 5445000, 5497928, 5551112, 5571122, 5685192, 5766408, 5896178, 5944352, 6111008, 6145149, 6202242, 6294152, 6315458, 6372450.

Some larger examples :