First numbers that belong to both sets:
1,
16,
25,
27,
32,
49,
64,
81,
121,
169,
289,
361,
529,
841,
961,
1000,
1125,
1152,
1225,
1296,
1323,
1372,
1568,
1600,
1728,
1944,
2000,
2025,
2304,
2500,
2592,
2744,
2916,
3087,
3136,
3200,
3375,
3456,
3888,
3969,
4000,
4608,
5000,
5184,
5488,
5625,
5832,
6075,
6125,
6272,
6400,
6912,
7776,
8000,
8575,
8748,
9261,
9604,
10648,
10816,
10952,
11236,
11552,
11979,
12321,
13225,
13448,
13456,
13689,
13924,
14161,
14283,
14792,
14884,
15125,
15129,
15376,
15488,
16641,
16928,
17576,
17672,
17689,
17956,
18432,
18496,
19652,
19773,
19881,
20164,
21025,
21125,
21296,
21316,
21632,
21904,
22472,
22707,
23104,
23409,
24025,
24964,
25281,
25600,
25921,
25947,
26896,
26912,
27436,
27556,
27648,
27848,
29241,
29403,
29584,
29768,
30752,
30976,
31329,
31684,
33275,
33489,
33856,
34225,
35152,
35344,
35912,
35937,
36125,
36864,
36963,
36992,
37636,
39304,
40328,
40401,
41067,
41209,
41503,
42025,
42592,
42632,
42849,
43264,
43808,
44217,
44944,
45125,
45369,
45387,
46208,
46225,
47089,
47961,
48668,
49923,
49928,
50176,
51200,
53792,
53824,
54872,
54925,
55112,
55225,
55296,
55696,
56169,
57967,
58564,
59168,
59319,
59536,
59643,
61504,
61731,
61952,
62001,
63368,
65219,
66125,
67081,
67712,
68121,
70225,
70227,
70304,
70688,
71289,
71824,
73728,
73984,
75272,
75625,
75843,
77841,
78608,
80656,
82369,
82944,
84681,
85184,
85264,
86528,
87025,
87616,
87723,
88209,
89888,
90601,
92416,
93025,
93987,
97336,
97556,
99127,
99856,
101761,
102152,
103041,
104329,
106276,
106929,
108000,
111132,
111556,
112500,
112896,
114921,
115200,
116281,
119716,
121500,
122500,
123904,
127008,
128164,
129032,
129600,
131044,
135000,
137200,
137288,
142129,
142884,
144000,
145161,
145800,
145924,
148176,
148996,
150152,
152881,
154449,
154568,
155236,
156800,
158404,
162000,
162409,
163216,
165375,
165649,
168921,
169344,
169744,
171500,
172800,
172872,
173056,
173889,
177608,
178084,
180000,
182408,
183184,
190096,
190512,
190969,
194400.
Some larger examples :
19700064,
19719200,
19756800,
19758025,
19769472,
19783872,
19794632,
19800500,
19810604,
19827925,
19830744,
19845000,
19873764,
19891600,
19895432,
19909444,
19920672,
19936225,
19961856,
19998784.