First numbers that belong to both sets:
1,
64,
729,
4096,
15625,
46656,
117649,
262144,
531441,
1000000,
1771561,
2985984,
4826809,
7529536,
11390625,
16777216,
24137569,
34012224,
47045881,
64000000,
85766121,
113379904,
148035889,
191102976,
244140625,
308915776,
387420489,
481890304,
594823321,
729000000,
887503681,
1073741824,
1291467969,
1544804416,
1838265625,
2176782336,
2565726409,
3010936384,
3518743761,
4096000000,
4750104241,
5489031744,
6321363049,
7256313856,
8303765625,
9474296896,
10779215329,
12230590464,
13841287201,
15625000000,
17596287801,
19770609664,
22164361129,
24794911296,
27680640625,
30840979456,
34296447249,
38068692544,
42180533641,
46656000000,
51520374361,
56800235584,
62523502209,
68719476736,
75418890625,
82653950016,
90458382169,
98867482624,
107918163081,
117649000000,
128100283921,
139314069504,
151334226289,
164206490176,
177978515625,
192699928576,
208422380089,
225199600704,
243087455521,
262144000000,
282429536481,
304006671424,
326940373369,
351298031616,
377149515625,
404567235136,
433626201009,
464404086784,
496981290961,
531441000000,
567869252041,
606355001344,
646990183449,
689869781056,
735091890625,
782757789696,
832972004929,
885842380864,
941480149401,
1000000000000,
1061520150601,
1126162419264,
1194052296529,
1265319018496,
1340095640625,
1418519112256,
1500730351849,
1586874322944,
1677100110841,
1771561000000,
1870414552161,
1973822685184,
2081951752609,
2194972623936,
2313060765625,
2436396322816,
2565164201769,
2699554153024,
2839760855281,
2985984000000,
3138428376721,
3297303959104,
3462825991689,
3635215077376,
3814697265625,
4001504141376,
4195872914689,
4398046511104,
4608273662721,
4826809000000,
5053913144281,
5289852801024,
5534900853769,
5789336458816,
6053445140625,
6327518887936,
6611856250609,
6906762437184,
7212549413161,
7529536000000,
7858047974841,
8198418170944,
8550986578849,
8916100448256,
9294114390625,
9685390482496,
10090298369529,
10509215371264,
10942526586601,
11390625000000,
11853911588401,
12332795428864,
12827693806929,
13339032325696,
13867245015625,
14412774445056,
14976071831449,
15557597153344,
16157819263041,
16777216000000,
17416274304961,
18075490334784,
18755369578009,
19456426971136,
20179187015625,
20924183895616,
21691961596369,
22483074023424,
23298085122481,
24137569000000,
25002110044521,
25892303048704,
26808753332089,
27752076864576,
28722900390625,
29721861554176,
30749609024289,
31806802621504,
32894113444921,
34012224000000,
35161828327081,
36343632130624,
37558352909169,
38806720086016,
40089475140625,
41407371740736,
42761175875209,
44151665987584,
45579633110361,
47045881000000,
48551226272641,
50096498540544,
51682540549249,
53310208315456,
54980371265625,
56693912375296,
58451728309129,
60254729561664,
62103840598801,
64000000000000,
65944160601201,
67937289638464,
69980368892329,
72074394832896,
74220378765625,
76419346977856,
78672340886049,
80980417183744,
83344647990241,
85766121000000,
88245939632761,
90785223184384,
93385106978409,
96046742518336,
98771297640625,
101559956668416,
104413920565969,
107334407093824,
110322650964681,
113379904000000,
116507435287321,
119706531338304,
122978496247489,
126324651851776,
129746337890625,
133244912166976,
136821750708889,
140478247931904,
144215816802121,
148035889000000,
151939915084881,
155929364660224,
160005726539569,
164170508913216,
168425239515625,
172771465793536,
177210755074809,
181744694737984,
186374892382561,
191102976000000,
195930594145441,
200859416110144,
205891132094649,
211027453382656,
216270112515625,
221620863468096,
227081481823729,
232653764952064,
238339532186001,
244140625000000,
250058907189001,
256096265048064,
262254607552729,
268535866540096,
274941996890625,
281474976710656,
288136807515649,
294929514414144,
301855146292441,
308915776000000,
316113500535561,
323450441233984,
330928743953809,
338550579265536,
346318142640625,
354233654641216,
362299361110569,
370517533364224,
378890468381881,
387420489000000,
396109944105121,
404961208827904,
413976684737889,
423158800038976,
432510009765625,
442032795979776,
451729667968489,
461603162442304,
471655843734321,
481890304000000.
Some larger examples :
686339028913329,
700321701542464,
714540961348201,
729000000000000,
743702041351801,
758650341657664,
773848189788129,
789298907447296,
805005849390625,
820972403643456,
837201991720249,
853698068844544,
870464124169641,
887503681000000,
904820297013361,
922417564483584,
940299110504209,
958468597212736,
976929722015625,
995686217814016.