First numbers that belong to both sets:
125,
128,
243,
256,
343,
512,
625,
729,
1024,
1029,
1215,
1250,
1280,
1331,
1369,
1458,
1536,
1681,
1701,
1715,
1792,
1849,
1875,
2048,
2187,
2197,
2209,
2401,
2560,
2809,
3125,
3481,
3584,
3645,
3721,
4096,
4374,
4375,
4489,
4802,
4913,
5041,
5103,
5329,
6241,
6250,
6561,
6859,
6889,
7203,
7921,
8192,
9375,
9409,
10000,
10082,
10112,
10125,
10201,
10206,
10240,
10368,
10375,
10443,
10449,
10496,
10609,
10624,
10625,
10633,
10658,
10752,
10935,
10976,
10985,
11008,
11045,
11125,
11163,
11392,
11421,
11449,
11664,
11767,
11776,
11875,
11881,
11907,
12005,
12032,
12125,
12167,
12288,
12393,
12416,
12482,
12500,
12544,
12691,
12769,
12800,
12879,
12943,
13122,
13125,
13467,
13568,
13718,
13778,
13824,
13851,
14045,
14063,
14336,
14337,
14375,
14406,
14641,
14739,
14749,
14823,
14848,
15104,
15123,
15309,
15379,
15463,
15552,
15616,
15625,
15842,
15872,
15987,
16000,
16121,
16129,
16281,
16384,
16767,
16807,
16875,
17152,
17161,
17253,
17405,
17496,
17739,
17920,
18125,
18176,
18179,
18225,
18605,
18688,
18723,
18750,
18769,
18818,
18944,
19197,
19208,
19321,
19375,
19663,
19683,
20000,
20169,
20224,
20237,
20480,
20577,
20667,
20736,
20923,
20992,
21141,
21248,
21609,
21627,
21870,
21875,
21952,
22016,
22201,
22445,
22599,
22784,
22801,
22981,
23125,
23328,
23571,
23763,
24010,
24057,
24064,
24334,
24353,
24367,
24389,
24565,
24576,
24649,
24832,
25000,
25039,
25088,
25205,
25515,
25625,
26047,
26244,
26411,
26569,
26645,
26875,
26973,
27097,
27136,
27783,
27889,
28125,
28227,
28431,
28469,
28561,
28672,
29282,
29375,
29791,
29889,
29929,
30208,
30375,
30527,
30618,
30625,
31104,
31205,
31213,
31232,
31250,
31347,
31423,
32000,
32041,
32761,
32768,
32805,
33125,
33271,
33614,
34263,
34295,
34304,
34375,
34391,
34445,
34992,
35287,
35721,
36015,
36352,
36481,
36501,
36875,
37179,
37249,
37303,
37376,
38125,
38416,
38637,
38809,
39366,
39601,
39605,
40000,
40448,
40625.
Some larger examples :
19996477,
19996672,
19996875,
19997199,
19997311,
19997354,
19997647,
19997928,
19997929,
19998125,
19998272,
19998657,
19998767,
19998976,
19999143,
19999291,
19999606,
19999872,
19999987,
20000000.