First numbers that belong to both sets:
1,
16,
25,
27,
32,
49,
64,
81,
121,
125,
128,
169,
243,
256,
289,
343,
361,
512,
529,
625,
729,
841,
961,
1000,
1024,
1225,
1296,
1331,
1369,
1600,
1681,
1728,
1849,
2025,
2048,
2187,
2197,
2209,
2304,
2401,
2500,
2744,
2809,
2916,
3125,
3136,
3375,
3481,
3721,
3969,
4096,
4489,
4913,
5041,
5184,
5329,
5625,
5832,
6241,
6400,
6561,
6859,
6889,
7776,
7921,
8000,
8192,
9261,
9409,
9604,
10000,
10201,
10609,
10648,
10816,
11236,
11449,
11664,
11881,
12167,
12321,
12544,
12769,
13225,
13456,
13689,
13824,
13924,
14161,
14641,
14884,
15129,
15376,
15625,
16129,
16384,
16641,
16807,
17161,
17576,
17689,
17956,
18225,
18496,
18769,
19321,
19683,
19881,
20164,
20736,
21025,
21316,
21609,
21904,
21952,
22201,
22801,
23104,
23409,
24025,
24389,
24649,
24964,
25281,
25600,
25921,
26244,
26569,
26896,
27556,
27889,
28561,
29241,
29584,
29791,
29929,
30625,
30976,
31329,
31684,
32041,
32761,
32768,
33489,
33856,
34225,
35344,
35721,
35937,
36481,
36864,
37249,
37636,
38416,
38809,
39304,
39601,
40000,
40401,
41209,
42025,
42849,
42875,
43264,
44521,
44944,
45369,
46225,
46656,
47089,
47961,
49729,
50176,
50625,
50653,
51529,
52441,
53824,
54289,
54872,
55225,
55696,
56169,
57121,
58081,
58564,
59049,
59319,
59536,
60025,
61504,
62001,
62500,
63001,
64000,
65536,
66049,
67081,
68121,
68921,
69169,
70225,
71289,
71824,
72361,
73441,
73984,
75625,
76729,
77841,
78125,
78961,
79507,
80089,
80656,
82369,
82944,
83521,
84681,
85184,
85264,
85849,
87025,
87616,
88209,
90601,
91125,
92416,
93025,
94249,
96721,
97336,
97969,
99856,
100000,
100489,
101761,
102400,
103041,
103823,
104329,
104976,
105625,
106276,
106929,
107584,
108241,
109561,
110224,
110592,
110889,
111556,
112225,
112896,
113569,
114244,
114921,
116281,
117649,
118336,
119716,
120409,
121801,
122500,
123201,
123904,
124609,
125000,
126025,
126736,
128164,
128881,
129600,
130321,
131044,
131072,
131769,
132651,
133225,
134689.
Some larger examples :
19802500,
19811401,
19829209,
19847025,
19855936,
19864849,
19873764,
19882681,
19891600,
19900521,
19902511,
19909444,
19918369,
19927296,
19936225,
19954089,
19963024,
19971961,
19989841,
19998784.