Search a number
balanced n.  and  perfect power

First numbers that belong to both sets:

9, 49, 169, 216, 225, 625, 676, 841, 961, 2744, 2916, 3125, 3249, 3721, 3969, 7225, 8649, 10609, 11881, 12100, 12321, 12769, 13924, 14641, 15625, 16129, 17689, 29241, 32400, 38025, 39601, 41209, 42849, 44944, 45369, 45796, 47524, 52900, 54872, 56644, 58081, 60516, 62001, 64009, 65025, 151321, 154449, 155236, 156025, 161604, 163216, 167281, 177241, 183184, 185761, 187489, 189225, 192721, 195112, 198916, 209764, 217156, 219024, 228484, 231361, 232324, 236196, 244036, 247009, 250000, 252004, 255025, 259081, 261121, 295936, 300304, 302500, 304704, 314721, 315844, 336400, 345744, 364816, 372100, 384400, 386884, 401956, 412164, 414736, 446224, 490000, 531441, 561001, 571787, 609961, 613089, 622521, 630436, 632025, 636804, 649636, 660969, 667489, 674041, 675684, 677329, 687241, 702244, 707281, 712336, 714025, 717409, 724201, 727609, 731025, 744769, 748225, 751689, 767376, 781456, 829921, 830584, 837225, 850084, 877969, 885481, 898704, 902500, 910116, 933156, 946729, 960400, 980100, 986049, 996004, 1012036, 1018081, 1028196, 1034289, 1042441, 1046529, 2211169, 2226064, 2248091, 2283121, 2301289, 2406104, 2418025, 2436721, 2442969, 2477476, 2486929, 2499561, 2518569, 2537649, 2544025, 2550409, 2553604, 2569609, 2579236, 2592100, 2608225, 2617924, 2739025, 2744000, 2745649, 2748964, 2782224, 2792241, 2798929, 2832489, 2845969, 2856100, 2862864, 2863288, 2879809, 2883204, 2903616, 2907025, 2927521, 2937796, 2944656, 2954961, 2961841, 2968729, 2989441, 2996361, 3013696, 3020644, 3034564, 3094081, 3101121, 3111696, 3171961, 3247204, 3265249, 3290596, 3305124, 3323329, 3326976, 3341584, 3345241, 3363556, 3367225, 3381921, 3392964, 3396649, 3426201, 3463321, 3467044, 3489424, 3493161, 3500641, 3508129, 3519376, 3523129, 3526884, 3534400, 3545689, 3568321, 3579664, 3581577, 3598609, 3613801, 3617604, 3721041, 3723875, 3724900, 3755844, 3763600, 3775249, 3794704, 3822025, 3829849, 3869893, 3888784, 3900625, 3928324, 3940225, 3960100, 4016016, 4056196, 4068289, 4084101, 4088484, 4120900, 4133089, 4153444, 4165681, 4169764, 4182025, 4190209, 4260096, 4372281, 4447881, 4502884, 4639716, 4656964, 4717584, 4778596, 4796100, 4848804, 4955076, 4977361, 5171076, 5207524, 5368489, 5382400, 5391684, 5400976, 5470921, 5494336, 5503716, 5541316, 5832225, 5987809, 6002500, 6007401, 6017209, 6041764.

Some larger examples :