First numbers that belong to both sets:
1,
16,
25,
49,
64,
81,
121,
169,
289,
361,
529,
841,
961,
1225,
1296,
1600,
2025,
2304,
2500,
2916,
3136,
3969,
5184,
5625,
6400,
9604,
10816,
11236,
12321,
13225,
13456,
13689,
13924,
14161,
14884,
15129,
15376,
16641,
17689,
17956,
18496,
19881,
20164,
21025,
21316,
21904,
23104,
23409,
24025,
24964,
25281,
25600,
25921,
26896,
27556,
29241,
29584,
30976,
31329,
31684,
33489,
33856,
34225,
35344,
36864,
37636,
40401,
41209,
42025,
42849,
43264,
44944,
45369,
46225,
47089,
47961,
50176,
53824,
55225,
55696,
56169,
58564,
59536,
61504,
62001,
67081,
68121,
70225,
71289,
71824,
73984,
75625,
77841,
80656,
82369,
82944,
84681,
85264,
87025,
87616,
88209,
90601,
92416,
93025,
99856,
101761,
103041,
104329,
106276,
106929,
111556,
112896,
114921,
116281,
119716,
122500,
123904,
128164,
129600,
131044,
142129,
142884,
145161,
145924,
148996,
152881,
154449,
155236,
158404,
162409,
163216,
165649,
168921,
169744,
173056,
173889,
178084,
183184,
190096,
190969,
198916,
199809,
202500,
203401,
204304,
205209,
206116,
209764,
217156,
221841,
223729,
228484,
231361,
232324,
239121,
240100,
243049,
251001,
252004,
254016,
255025,
258064,
264196,
265225,
267289,
269361,
274576,
275625,
276676,
277729,
284089,
286225,
288369,
289444,
291600,
293764,
294849,
295936,
297025,
300304,
303601,
306916,
309136,
312481,
313600,
315844,
319225,
320356,
328329,
335241,
339889,
343396,
345744,
346921,
349281,
355216,
356409,
360000,
364816,
369664,
373321,
376996,
386884,
391876,
394384,
395641,
400689,
401956,
403225,
421201,
425104,
429025,
438244,
444889,
446224,
447561,
450241,
454276,
463761,
469225,
471969,
474721,
478864,
481636,
483025,
485809,
487204,
488601,
490000,
494209,
495616,
498436,
499849,
508369,
512656,
514089,
515524,
518400,
519841,
522729,
524176,
534361,
538756,
540225,
541696,
543169,
555025,
556516,
561001,
562500,
567009,
570025,
571536,
574564,
582169,
583696,
586756,
588289,
594441,
595984,
605284,
606841,
609961,
616225,
620944,
622521,
625681,
628849,
630436,
633616,
638401,
643204,
644809,
651249,
652864,
656100,
660969,
664225,
667489,
669124.
Some larger examples :
19316025,
19324816,
19342404,
19377604,
19386409,
19395216,
19430464,
19448100,
19501056,
19624900,
19633761,
19660356,
19686969,
19695844,
19758025,
19873764,
19891600,
19909444,
19936225,
19998784.