First numbers that belong to both sets:
1,
4,
8,
9,
16,
25,
27,
32,
49,
64,
81,
121,
125,
128,
169,
225,
243,
256,
289,
343,
361,
441,
484,
512,
529,
625,
676,
729,
841,
961,
1024,
1089,
1156,
1225,
1331,
1369,
1444,
1521,
1681,
1849,
2025,
2048,
2116,
2187,
2197,
2209,
2401,
2601,
2809,
3025,
3125,
3249,
3364,
3375,
3481,
3721,
3844,
3969,
4096,
4225,
4489,
4761,
4913,
5041,
5329,
5476,
5625,
5929,
6241,
6561,
6724,
6859,
6889,
7225,
7396,
7569,
7921,
8192,
8281,
8649,
8836,
9025,
9261,
9409,
9801,
10201,
10609,
11236,
11449,
11881,
12167,
12321,
12769,
13225,
13689,
13924,
14161,
14641,
14884,
15129,
15625,
16129,
16384,
16641,
16807,
17161,
17689,
17956,
18225,
18769,
19321,
19683,
19881,
20164,
20449,
21025,
21316,
21609,
21904,
22201,
22801,
23409,
24025,
24389,
24649,
24964,
25281,
25921,
26569,
26896,
27225,
27556,
27889,
28561,
29241,
29584,
29791,
29929,
30625,
31329,
31684,
32041,
32761,
32768,
33489,
34225,
34969,
35344,
35721,
35937,
36481,
37249,
37636,
38025,
38809,
39304,
39601,
40401,
40804,
41209,
42025,
42436,
42849,
42875,
43681,
44521,
44944,
45369,
45796,
46225,
47089,
47524,
47961,
48841,
49729,
50625,
50653,
51076,
51529,
52441,
53361,
54289,
54872,
55225,
55696,
56169,
57121,
58081,
58564,
59049,
59319,
59536,
60025,
61009,
62001,
63001,
64009,
64516,
65025,
65536,
66049,
67081,
68121,
68644,
68921,
69169,
70225,
71289,
71824,
72361,
73441,
74529,
75076,
75625,
76729,
77284,
77841,
78125,
78961,
79507,
80089,
80656,
81225,
82369,
83521,
84681,
85264,
85849,
87025,
88209,
88804,
89401,
90601,
91125,
91204,
91809,
93025,
94249,
95481,
96721,
97336,
97969,
98596,
99856,
100489,
101761,
103041,
103823,
104329,
105625,
106276,
106929,
108241,
109561,
110224,
110889,
111556,
112225,
113569,
114244,
114921,
116281,
117649,
119025,
119716,
120409,
121801,
123201,
124609,
126025,
126736,
127449,
128164,
128881,
130321,
131044,
131072,
131769,
132651,
133225.
Some larger examples :
9815689,
9821956,
9840769,
9853321,
9865881,
9872164,
9878449,
9891025,
9903609,
9909904,
9916201,
9928801,
9938375,
9941409,
9947716,
9954025,
9966649,
9972964,
9979281,
9991921.