First numbers that belong to both sets:
125,
128,
256,
512,
625,
729,
1024,
1029,
1280,
1369,
1536,
1681,
1701,
1792,
1849,
2048,
2197,
2209,
2401,
2560,
2809,
3125,
3481,
3584,
3645,
3721,
4096,
4489,
4913,
5041,
5329,
6241,
6561,
6889,
7921,
8192,
9409,
10000,
10112,
10125,
10201,
10240,
10368,
10449,
10496,
10609,
10624,
10625,
10633,
10752,
10976,
10985,
11008,
11045,
11125,
11392,
11421,
11449,
11664,
11776,
11881,
12005,
12032,
12125,
12288,
12393,
12416,
12500,
12544,
12769,
12800,
13125,
13568,
13824,
14045,
14336,
14337,
14641,
14749,
14848,
15104,
15309,
15552,
15616,
15625,
15872,
16000,
16121,
16129,
16281,
16384,
17152,
17161,
17253,
17405,
17496,
17920,
18125,
18176,
18225,
18605,
18688,
18769,
18944,
19197,
19208,
19321,
20000,
20169,
20224,
20237,
20480,
20577,
20736,
20992,
21141,
21248,
21609,
21952,
22016,
22201,
22445,
22784,
22801,
22981,
23125,
23328,
24057,
24064,
24353,
24389,
24565,
24576,
24649,
24832,
25000,
25088,
25205,
25625,
26244,
26569,
26645,
26973,
27097,
27136,
27889,
28125,
28469,
28561,
28672,
29889,
29929,
30208,
30625,
31104,
31205,
31213,
31232,
32000,
32041,
32761,
32768,
32805,
33125,
34304,
34445,
34992,
35721,
36352,
36481,
36501,
37249,
37376,
38125,
38416,
38637,
38809,
39601,
39605,
40000,
40448,
40625,
40817,
40960,
41472,
41553,
42496,
43904,
44469,
44521,
45568,
45625,
46656,
47045,
48013,
49152,
49664,
49729,
50000,
50301,
50421,
50625,
50653,
51529,
52441,
52488,
53125,
53217,
54289,
55625,
57121,
57344,
58081,
59049,
60025,
60625,
62208,
62500,
63001,
64000,
64881,
65536,
65625,
66049,
67228,
67797,
68921,
69169,
69629,
69984,
70713,
72361,
73205,
73441,
76545,
76729,
76832,
78125,
78732,
78961,
80000,
80089,
81920,
83349,
83521,
85169,
85293,
85849,
87808,
88837,
89373,
90625,
91125,
93312,
94041,
94249,
96721,
97969,
98304,
98441,
100000,
100352,
100489,
100625,
100736,
100845,
100864,
100949,
101120,
101125,
101185,
101632,
101817,
101888,
102016,
102400,
102541,
102625,
102656,
102789.
Some larger examples :
999948288,
999951673,
999951872,
999952128,
999953033,
999953125,
999955449,
999960224,
999960641,
999961277,
999964197,
999964672,
999970505,
999976192,
999978125,
999981056,
999981693,
999990625,
999995456,
999999189.