First numbers that belong to both sets:
125,
128,
243,
256,
343,
512,
625,
729,
1024,
1029,
1250,
1331,
1369,
1681,
1849,
1875,
2048,
2187,
2197,
2209,
2401,
2809,
3125,
3481,
3721,
4096,
4375,
4489,
4802,
4913,
5041,
5103,
5329,
6241,
6561,
6859,
6889,
7203,
7921,
8192,
9409,
10000,
10082,
10201,
10375,
10443,
10449,
10609,
10625,
10633,
10658,
11045,
11449,
11664,
11767,
11881,
12005,
12125,
12167,
12482,
12691,
12769,
12800,
12943,
13125,
13778,
13851,
14045,
14375,
14641,
14749,
14823,
15123,
15309,
15463,
15625,
15842,
16121,
16129,
16281,
16384,
16807,
17161,
17405,
17739,
18179,
18225,
18605,
18769,
18818,
19197,
19208,
19321,
19375,
19683,
20000,
20237,
20577,
20667,
20736,
20923,
21609,
22201,
22445,
22599,
22801,
22981,
23125,
23571,
23763,
24353,
24367,
24389,
24649,
25039,
25088,
25205,
25625,
26047,
26244,
26411,
26569,
26645,
26875,
26973,
27097,
27783,
27889,
28431,
28561,
29282,
29375,
29791,
29929,
30527,
30625,
31205,
31250,
31347,
32041,
32761,
32768,
33125,
34375,
34391,
34445,
35287,
36481,
37249,
37303,
38125,
38416,
38809,
39601,
39605,
40000,
40625,
40817,
41553,
41875,
43923,
44469,
44521,
45619,
45625,
45927,
46656,
46875,
47045,
48013,
48223,
48843,
49729,
50625,
50653,
51529,
51875,
52441,
53125,
53217,
54289,
55223,
55447,
57121,
57122,
57591,
58081,
59049,
60025,
60625,
62500,
63001,
64827,
65536,
65863,
66049,
67797,
68921,
69169,
69629,
70713,
71875,
72361,
73441,
74431,
76729,
78125,
78961,
79507,
80089,
80919,
83521,
84035,
85169,
85683,
85849,
88837,
89373,
94041,
94249,
96721,
97969,
100489,
100625,
100949,
101251,
101331,
101375,
101875,
102303,
102400,
102487,
102541,
102625,
102875,
102973,
103058,
103243,
103247,
103259,
103375,
103499,
103823,
103933,
104375,
104882,
104976,
105125,
105149,
105219,
105625,
105861,
106097,
106625,
106673,
106677,
107125,
107359,
107584,
107648,
107875,
107909,
107911,
108125,
108151,
108241,
108578,
108731,
109091,
109375,
109443,
109561,
109625,
110079,
110125,
110224,
110375,
110473,
110875,
111005.
Some larger examples :
9966551,
9967789,
9969987,
9971353,
9971875,
9974759,
9974907,
9975101,
9978641,
9979985,
9985759,
9988029,
9988463,
9988487,
9989107,
9990299,
9992501,
9993947,
9998677,
9999803.