First numbers that belong to both sets:
1,
4,
8,
16,
36,
243,
324,
400,
441,
1296,
2809,
2916,
3481,
4624,
4900,
5184,
6889,
7776,
8192,
11236,
11881,
13689,
17689,
19600,
19683,
20736,
21904,
24025,
25921,
34969,
39204,
45796,
47089,
47524,
47961,
56169,
59536,
72361,
73984,
78961,
87616,
95481,
97336,
106929,
114921,
120409,
127449,
141376,
147456,
154449,
160000,
175616,
184041,
190096,
196249,
197136,
203401,
224676,
272484,
274625,
293764,
311364,
346921,
350464,
356409,
379456,
386884,
390625,
391876,
393129,
400689,
405224,
405769,
412164,
451584,
469225,
484416,
493039,
501264,
527076,
553536,
585225,
592900,
616225,
672400,
680625,
692224,
704969,
708964,
712336,
765625,
779689,
781456,
788544,
940900,
950625,
1000000,
1010025,
1032256,
1094116,
1104601,
1108809,
1147041,
1168561,
1183744,
1194649,
1196836,
1279161,
1299600,
1320201,
1387684,
1454436,
1498176,
1540081,
1547536,
1595169,
1602756,
1682209,
1687401,
1703025,
1817104,
1830609,
1893376,
1898884,
1912689,
1934881,
1946025,
1954404,
2131600,
2140369,
2196324,
2229049,
2247001,
2328676,
2505889,
2582449,
2598544,
2621161,
2640625,
2653641,
2669956,
2679769,
2719201,
2725801,
2768896,
2835856,
2856100,
2900209,
2941225,
3062500,
3097600,
3101121,
3112136,
3189796,
3222025,
3448449,
3511876,
3545689,
3694084,
3701776,
3728761,
3748096,
3763600,
3924361,
3980025,
4028049,
4084101,
4293184,
4359744,
4368100,
4376464,
4397409,
4435236,
4447881,
4562496,
4566769,
4579600,
4809249,
4848804,
4875264,
4913000,
5026564,
5067001,
5116644,
5121169,
5180176,
5331481,
5405625,
5484964,
5508409,
5517801,
5569600,
5583769,
5635876,
5760000,
6002500,
6022116,
6280036,
6330256,
6335289,
6345361,
6360484,
6385729,
6461764,
6466849,
6594624,
6708100,
6801664,
6806881,
6859000,
6890625,
6895876,
6911641,
6943225,
7077888,
7134241,
7177041,
7198489,
7230721,
7284601,
7431076,
7739524,
7800849,
7918596,
7929856,
8000000,
8116801,
8271376,
8282884,
8294400,
8381025,
8386816,
8468100,
8503056,
8526400,
8590761,
8602489,
8661249,
8755681,
8814961,
8826841,
8946081,
9090225,
9162729,
9290304,
9363600,
9443329,
9486400,
9504889,
9690769,
9759376,
9796900.