First numbers that belong to both sets:
625,
1029,
1250,
1280,
1536,
1681,
1715,
1792,
1849,
1875,
2187,
2197,
2401,
2560,
3481,
3584,
4374,
4489,
4802,
5041,
6241,
9409,
10000,
10082,
10112,
10240,
10368,
10443,
10496,
10609,
10625,
10752,
11045,
11767,
11907,
12032,
12288,
12416,
12482,
12544,
12691,
12769,
12800,
13125,
14063,
14336,
14375,
14641,
15104,
15379,
15616,
15625,
15872,
16121,
16129,
16807,
17152,
17161,
17253,
17496,
17739,
17920,
18225,
18605,
18688,
18818,
18944,
19208,
20000,
20224,
20480,
20577,
20736,
20992,
21141,
21609,
22599,
23571,
24057,
24064,
24367,
24576,
24649,
24832,
25088,
26047,
28125,
28672,
29282,
29375,
29889,
30208,
31213,
31232,
31250,
32761,
33614,
34304,
34375,
34445,
34992,
35721,
36875,
37249,
37376,
38416,
40000,
40448,
40960,
41472,
42875,
43011,
48223,
48843,
49152,
49664,
49729,
50625,
51529,
57344,
59375,
62500,
64881,
65625,
66049,
67228,
67797,
69169,
69984,
70713,
71875,
73167,
73205,
76832,
80000,
81920,
90625,
91125,
94041,
94249,
96875,
97969,
98304,
98441,
100352,
100499,
100736,
101120,
101125,
101185,
101250,
101375,
101632,
101875,
101888,
102400,
102541,
102625,
102789,
103058,
103173,
103375,
103552,
103680,
103936,
104704,
104960,
105149,
105344,
105856,
106112,
106240,
106496,
106625,
106673,
107264,
107359,
107375,
107584,
107648,
107653,
107776,
108032,
108151,
109056,
109503,
109760,
109952,
110336,
110375,
110848,
111104,
111392,
112000,
112023,
112256,
112384,
112509,
112627,
112847,
112999,
113024,
113125,
113375,
113408,
113533,
113627,
113875,
113920,
114005,
114176,
114453,
114688,
116224,
116608,
116992,
117128,
117248,
117625,
117632,
117855,
118125,
118336,
118375,
118528,
118579,
118750,
118803,
118912,
119296,
119313,
119707,
120000,
120125,
120448,
120771,
120832,
121203,
121216,
121375,
121765,
121801,
121835,
121984,
122368,
122451,
123008,
123201,
123392,
123776,
123875,
124288,
124672,
124928,
125000,
125625,
125696,
126603,
126875,
126976,
127575,
127616,
127744,
127939,
128512,
128625,
129762,
129997,
130235,
130891,
131250,
131279,
131369,
131383,
131584,
131712,
131769,
132098,
132608,
132651.
Some larger examples :
9918531,
9921875,
9923847,
9926405,
9933354,
9937739,
9938999,
9940625,
9945088,
9948663,
9949744,
9961472,
9962743,
9974759,
9984375,
9988463,
9988487,
9990299,
9996777,
9999803.