First numbers that belong to both sets:
1,
16,
25,
27,
32,
49,
64,
81,
121,
125,
128,
169,
243,
256,
289,
343,
361,
512,
529,
625,
729,
841,
961,
1000,
1024,
1125,
1152,
1225,
1296,
1323,
1331,
1369,
1372,
1568,
1600,
1681,
1728,
1849,
1944,
2000,
2025,
2048,
2187,
2197,
2209,
2304,
2401,
2500,
2592,
2744,
2809,
2916,
3087,
3125,
3136,
3200,
3375,
3456,
3481,
3721,
3888,
3969,
4000,
4096,
4489,
4608,
4913,
5000,
5041,
5184,
5329,
5488,
5625,
5832,
6075,
6125,
6241,
6272,
6400,
6561,
6859,
6889,
6912,
7776,
7921,
8000,
8192,
8575,
8748,
9261,
9409,
9604,
10000,
10125,
10201,
10368,
10609,
10648,
10816,
10952,
10976,
11236,
11449,
11552,
11664,
11881,
11907,
11979,
12167,
12321,
12500,
12544,
12769,
12800,
13225,
13448,
13456,
13689,
13824,
13924,
14161,
14283,
14641,
14792,
14884,
15125,
15129,
15376,
15488,
15552,
15625,
16000,
16129,
16384,
16641,
16807,
16875,
16928,
17161,
17496,
17576,
17672,
17689,
17956,
18225,
18432,
18496,
18769,
19208,
19321,
19652,
19683,
19773,
19881,
20000,
20164,
20736,
21025,
21125,
21296,
21316,
21609,
21632,
21904,
21952,
22201,
22472,
22707,
22801,
23104,
23328,
23409,
24025,
24389,
24649,
24964,
25000,
25088,
25281,
25600,
25921,
25947,
26244,
26569,
26896,
26912,
27436,
27556,
27648,
27783,
27848,
27889,
28125,
28561,
29241,
29403,
29584,
29768,
29791,
29929,
30375,
30625,
30752,
30976,
31104,
31329,
31684,
32000,
32041,
32761,
32768,
33275,
33489,
33856,
34225,
34992,
35152,
35344,
35721,
35912,
35937,
36125,
36481,
36864,
36963,
36992,
37249,
37636,
38416,
38809,
39304,
39601,
40000,
40328,
40401,
41067,
41209,
41472,
41503,
42025,
42592,
42632,
42849,
42875,
43264,
43808,
43904,
44217,
44521,
44944,
45125,
45369,
45387,
46208,
46225,
46656,
47089,
47961,
48668,
49729,
49923,
49928,
50000,
50176,
50625,
50653,
51200,
51529,
52441,
52488,
53792,
53824,
54289,
54675,
54872,
54925,
55112,
55225,
55296,
55696.
Some larger examples :
19895432,
19900521,
19902511,
19909444,
19918169,
19918369,
19920672,
19921783,
19922787,
19927296,
19936225,
19945928,
19954089,
19961856,
19963024,
19971200,
19971961,
19989841,
19998784,
20000000.