First numbers that belong to both sets:
1,
4,
8,
9,
27,
36,
81,
100,
144,
216,
225,
243,
324,
400,
441,
512,
576,
900,
1000,
1296,
1521,
1728,
1764,
2025,
2304,
2401,
2601,
2704,
2916,
3600,
3969,
4225,
4356,
4624,
4913,
5184,
5832,
6084,
6400,
7056,
7744,
7776,
8000,
8100,
9216,
10000,
10404,
10816,
11025,
11664,
12100,
12321,
12544,
13689,
13824,
14400,
15876,
17424,
17576,
19044,
19600,
19683,
20736,
21904,
22500,
24336,
26244,
27000,
28224,
30276,
32400,
33124,
35937,
36100,
39204,
40000,
40401,
41616,
42849,
44100,
46656,
48400,
54756,
57600,
59049,
59319,
60516,
61504,
62001,
63504,
64000,
69696,
72900,
74088,
75625,
77841,
82944,
88209,
90000,
93636,
99225,
100000,
101124,
103041,
104329,
104976,
108900,
110592,
110889,
116964,
121104,
122500,
123201,
125000,
125316,
129600,
139876,
142884,
152100,
156816,
157464,
161604,
164836,
171396,
176400,
177147,
185193,
186624,
188356,
194481,
198025,
202500,
211600,
213444,
216000,
219024,
226576,
227529,
230400,
234256,
236196,
240100,
242064,
244036,
248004,
248832,
251001,
254016,
256036,
260100,
263169,
270400,
272484,
278784,
279936,
281961,
283024,
286225,
287496,
291600,
295936,
297025,
301401,
302500,
304704,
311364,
314432,
321489,
324900,
328509,
331776,
336400,
343000,
352836,
360000,
363609,
373248,
374544,
385641,
389376,
390625,
396900,
412164,
419904,
421875,
422500,
425104,
431649,
432964,
435600,
442225,
443556,
448900,
455625,
459684,
462400,
465124,
467856,
474552,
476100,
480249,
492804,
501264,
504100,
508369,
509796,
512000,
518400,
525625,
544644,
558009,
562500,
571536,
577600,
585225,
589824,
592704,
592900,
599076,
608400,
613089,
614656,
617796,
627264,
640000,
648025,
656100,
658503,
664225,
665856,
670761,
675684,
685584,
695556,
700569,
705600,
715716,
729000,
729316,
739600,
746496,
762129,
767376,
774400,
777924,
788544,
799236,
804357,
810000,
813604,
819025,
826281,
842724,
853776,
876096,
883600,
884736,
887364,
893025,
898704,
910116,
921600,
944784,
956484,
962361,
968256,
970225,
972196,
980100,
984064,
990025,
998001,
1000000,
1004004,
1008016,
1010025,
1014049,
1016064,
1020100,
1022121.
Some larger examples :
9974016900,
9976014400,
9976413924,
9977013225,
9980010000,
9982207921,
9983007225,
9983606724,
9984006400,
9985005625,
9986004900,
9986804356,
9987204096,
9989003025,
9992001600,
9994400784,
9995000625,
9997600144,
9998000100,
10000000000.