First numbers that belong to both sets:
9,
49,
169,
216,
225,
625,
676,
841,
961,
2744,
2916,
3125,
3249,
3721,
3969,
7225,
8649,
10609,
11881,
12100,
12321,
12769,
13924,
14641,
15625,
16129,
17689,
29241,
32400,
38025,
39601,
41209,
42849,
44944,
45369,
45796,
47524,
52900,
54872,
56644,
58081,
60516,
62001,
64009,
65025,
151321,
154449,
155236,
156025,
161604,
163216,
167281,
177241,
183184,
185761,
187489,
189225,
192721,
195112,
198916,
209764,
217156,
219024,
228484,
231361,
232324,
236196,
244036,
247009,
250000,
252004,
255025,
259081,
261121,
295936,
300304,
302500,
304704,
314721,
315844,
336400,
345744,
364816,
372100,
384400,
386884,
401956,
412164,
414736,
446224,
490000,
531441,
561001,
571787,
609961,
613089,
622521,
630436,
632025,
636804,
649636,
660969,
667489,
674041,
675684,
677329,
687241,
702244,
707281,
712336,
714025,
717409,
724201,
727609,
731025,
744769,
748225,
751689,
767376,
781456,
829921,
830584,
837225,
850084,
877969,
885481,
898704,
902500,
910116,
933156,
946729,
960400,
980100,
986049,
996004,
1012036,
1018081,
1028196,
1034289,
1042441,
1046529,
2211169,
2226064,
2248091,
2283121,
2301289,
2406104,
2418025,
2436721,
2442969,
2477476,
2486929,
2499561,
2518569,
2537649,
2544025,
2550409,
2553604,
2569609,
2579236,
2592100,
2608225,
2617924,
2739025,
2744000,
2745649,
2748964,
2782224,
2792241,
2798929,
2832489,
2845969,
2856100,
2862864,
2863288,
2879809,
2883204,
2903616,
2907025,
2927521,
2937796,
2944656,
2954961,
2961841,
2968729,
2989441,
2996361,
3013696,
3020644,
3034564,
3094081,
3101121,
3111696,
3171961,
3247204,
3265249,
3290596,
3305124,
3323329,
3326976,
3341584,
3345241,
3363556,
3367225,
3381921,
3392964,
3396649,
3426201,
3463321,
3467044,
3489424,
3493161,
3500641,
3508129,
3519376,
3523129,
3526884,
3534400,
3545689,
3568321,
3579664,
3581577,
3598609,
3613801,
3617604,
3721041,
3723875,
3724900,
3755844,
3763600,
3775249,
3794704,
3822025,
3829849,
3869893,
3888784,
3900625,
3928324,
3940225,
3960100,
4016016,
4056196,
4068289,
4084101,
4088484,
4120900,
4133089,
4153444,
4165681,
4169764,
4182025,
4190209,
4260096,
4372281,
4447881,
4502884,
4639716,
4656964,
4717584,
4778596,
4796100,
4848804,
4955076,
4977361,
5171076,
5207524,
5368489,
5382400,
5391684,
5400976,
5470921,
5494336,
5503716,
5541316,
5832225,
5987809,
6002500,
6007401,
6017209,
6041764.
Some larger examples :
197374401,
197402500,
197458704,
197767969,
197908624,
197964900,
198077476,
198387225,
198528100,
198725409,
198810000,
198894609,
199204996,
199317924,
199430884,
199459129,
199656900,
199713424,
199939600,
199967881.