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Curzon n.  and  perfect power

First numbers that belong to both sets:

1, 9, 81, 125, 441, 729, 1089, 2025, 5625, 7569, 8649, 9261, 9801, 11025, 15129, 18225, 23409, 24389, 31329, 35721, 40401, 47961, 56169, 65025, 74529, 81225, 88209, 103041, 106929, 123201, 127449, 140625, 149769, 154449, 159201, 164025, 173889, 178929, 184041, 185193, 194481, 233289, 239121, 269361, 288369, 308025, 342225, 356409, 385641, 400689, 431649, 456533, 480249, 488601, 497025, 540225, 576081, 585225, 613089, 660969, 670761, 700569, 720801, 783225, 804609, 904401, 927369, 986049, 1022121, 1034289, 1134225, 1199025, 1252161, 1279161, 1334025, 1361889, 1390041, 1418481, 1520289, 1625625, 1671849, 1687401, 1718721, 1766241, 1814409, 1846881, 1896129, 1912689, 1946025, 1979649, 2013561, 2030625, 2047761, 2082249, 2169729, 2277081, 2295225, 2387025, 2424249, 2576025, 2692881, 2712609, 2752281, 2832489, 3038049, 3059001, 3101121, 3164841, 3207681, 3307949, 3493161, 3560769, 3583449, 3651921, 3697929, 3837681, 4028049, 4100625, 4173849, 4297329, 4347225, 4372281, 4492125, 4549689, 4601025, 4626801, 4652649, 4730625, 4888521, 5076009, 5239521, 5349969, 5433561, 5461569, 5602689, 5919489, 6007401, 6066369, 6331625, 6456681, 6487209, 6610041, 6671889, 6796449, 7080921, 7177041, 7306209, 7436529, 7568001, 7645373, 7700625, 7733961, 7901721, 8003241, 8311689, 8415801, 8590761, 9054081, 9235521, 9418761, 9566649, 9678321, 10017225, 10055241, 10284849, 10439361, 10478169, 10595025, 10793861, 10870209, 11029041, 11309769, 11471769, 11553201, 11634921, 11840481, 11923209, 12006225, 12173121, 12215025, 12257001, 12552849, 12766329, 12895281, 12938409, 13155129, 13312053, 13373649, 13995081, 14356521, 14402025, 14447601, 14630625, 14676561, 14814801, 14907321, 15093225, 15186609, 15438249, 15657849, 15752961, 15848361, 15992001, 16040025, 16475481, 16524225, 16573041, 16670889, 16769025, 17015625, 17114769, 17214201, 17514225, 17564481, 18071001, 18429849, 18584721, 19158129, 19263321, 19465109, 19847025, 19900521, 19954089, 20115225, 20223009, 20439441, 20511149, 20930625, 21040569, 21316689, 21594609, 21762225, 22325625, 22496049, 22838841, 23242041, 23299929, 23882769, 24117921, 24235929, 24295041, 24710841, 24770529, 24890121, 24950025, 25070049, 25250625, 25492401, 25553025, 25796241, 25918281, 26198073, 26224641, 26471025, 26594649, 26780625, 26904969, 26967249, 27217089, 27405225, 27657081, 28227969, 28483569, 29062881, 29192409, 29322225, 29582721, 29713401, 30107169, 30437289, 30835809, 31979025, 32251041, 32867289, 33076161, 33281361, 33489369, 33977241, 34047225, 34468641.

Some larger examples :