First numbers that belong to both sets:
25,
121,
125,
128,
289,
343,
625,
1024,
1255,
1285,
1296,
2048,
2187,
2500,
2501,
2507,
2509,
2737,
2916,
3125,
3281,
3685,
4096,
4167,
4624,
5776,
6455,
8192,
9025,
9216,
9261,
10201,
10525,
11259,
11663,
11664,
11665,
11943,
12091,
12100,
12167,
12337,
12493,
12505,
12769,
12955,
13125,
13225,
13243,
13725,
13813,
13823,
14035,
14129,
14175,
14641,
14647,
15125,
15613,
15623,
15625,
15627,
15631,
15633,
15655,
15689,
15697,
16347,
16375,
16384,
16387,
16479,
16743,
16783,
16807,
17437,
18225,
18265,
19321,
19453,
19629,
19683,
19693,
20485,
20736,
21845,
21953,
22757,
24339,
24367,
24375,
24385,
24389,
24964,
25105,
26244,
26896,
26973,
27783,
27889,
28322,
28561,
28900,
29282,
29519,
29523,
29525,
29549,
29584,
29768,
29929,
30625,
31250,
31347,
32747,
32751,
32759,
32761,
32765,
32768,
32815,
32825,
32849,
32855,
32875,
32885,
33655,
34991,
34993,
36864,
37187,
37249,
37449,
38416,
39283,
41323,
41665,
42025,
43264,
43375,
43689,
43775,
44977,
45363,
45365,
45369,
45873,
45927,
45947,
45957,
46613,
46615,
46637,
46641,
46651,
46655,
46656,
46657,
46661,
46673,
46677,
46875,
52429,
52483,
52493,
53245,
53297,
53824,
54953,
55225,
58957,
58973,
59039,
59045,
59049,
59057,
59129,
59147,
59319,
59759,
61435,
62503,
63895,
63985,
65471,
65483,
65485,
65489,
65491,
65531,
65536,
67149,
68644,
69253,
69895,
69985,
70225,
73984,
74183,
75433,
76835,
77459,
78055,
78123,
78125,
78133,
78545,
78659,
82944,
83521,
83957,
85264,
87381,
91853,
93217,
97333,
97343,
98305,
98375,
98435,
100255,
100525,
101299,
102391,
102487,
102541,
102595,
102783,
103823,
104329,
104375,
104897,
104969,
104976,
104979,
104995,
105025,
105625,
106289,
107329,
107584,
108241,
109351,
109353,
109355,
109375,
112505,
112509,
112895,
112923,
114242,
114244,
114245,
114395,
114627,
114647,
114681,
114779,
114921,
115625,
115699,
116317,
116635,
116729,
116837,
117067,
117128,
117475,
117567,
117575,
117587,
117597,
117613,
117623,
117625,
117635,
117637,
117639,
117641,
117647.
Some larger examples :
976523,
976529,
976539,
976563,
976573,
976583,
976593,
978121,
978671,
979769,
983041,
983045,
983047,
984375,
986947,
990025,
992016,
995331,
995333,
999163.