First numbers that belong to both sets:
361,
1600,
2401,
2500,
16000,
25000,
33124,
39200,
39601,
81225,
102400,
130321,
135200,
143641,
160000,
161604,
171500,
207025,
250000,
283024,
308025,
323208,
392000,
406125,
480200,
546121,
612500,
731025,
780300,
1024000,
1095200,
1137032,
1147041,
1201216,
1352000,
1391112,
1540125,
1560600,
1600000,
1715000,
2030625,
2050624,
2080800,
2112500,
2223081,
2340900,
2500000,
2528100,
2592100,
3052009,
3240125,
3441123,
3493161,
3591200,
3901500,
3920000,
3996001,
4161600,
4263200,
4421700,
4512500,
4631104,
4802000,
4831204,
5056200,
5105212,
6022116,
6111008,
6125000,
6242400,
6245001,
6260004,
6502500,
7022700,
7128900,
7300804,
7527200,
7803000,
8323200,
8910225,
9210632,
10042561,
10153125,
10161032,
10240000,
10621081,
10952000,
11007432,
11704500,
12012500,
12044232,
12355225,
12440072,
12520008,
12640500,
12903200,
13265100,
13354112,
13520000,
13610700,
13764100,
14045400,
14257800,
14300552,
15103008,
15606000,
16000000,
16232841,
16601200,
17056900,
17112500,
17150000,
20025625,
20151121,
20224800,
20304036,
20421361,
20608200,
20711601,
20720704,
20808000,
21068100,
21125000,
21206025,
21255200,
21386700,
21735224,
22052416,
22108500,
22934521,
23112500,
23409000,
24452127,
24512401,
24700900,
25000000,
25040016,
25281000,
25921000,
26530200,
27221400,
28515600,
30195025,
30201992,
30206016,
30239001,
30337200,
30912300,
31047184,
31680800,
32004500,
32319225,
32364721,
32512500,
33200644,
33663204,
33756100,
34234201,
34445161,
34928100,
35113500,
35462025,
35644500,
35912000,
36048016,
36216324,
38812900,
39015000,
39200000,
40522400,
40832100,
41216400,
41616000,
42003361,
42016324,
42136200,
42390243,
42632000,
42773400,
44217000,
44551125,
44609041,
45024100,
45125000,
45630025,
47760300,
48020000,
50080032,
50353216,
50562000,
51344307,
51520500,
53060400,
53127432,
53363025,
53436100,
56085121,
56112500,
56310016,
60000516,
60152600,
60372900,
60412032,
61250000,
61383200,
62424000,
63202500,
63204300,
63303752,
63680400,
64071200,
64240225,
65025000,
65124900,
70227000,
70375321,
71289000,
72131049,
72216004,
75272000,
75516100,
78012500,
78030000,
79600500,
80192025,
81036004,
83232000,
84621601,
86510700,
90611361,
90630400,
91011600,
95520600.