1, 4 = 2^2, 8 = 2^3, 9 = 3^2, 16 = 4^2 =2^4, 25 = 5^2, 27 = 3^3, 32 =2^5, 36 = 6^2, 49 = 7^2, 64 = 8^2 = 4^3 =2^6, 81 = 9^2 =3^4, 100 =10^2, 121 =11^2, 125 = 5^3, 128 =2^7, 144 =12^2, 169 =13^2, 196 =14^2, 216 = 6^3, 225 =15^2, 243 =3^5, 256 =16^2 =4^4 =2^8, 289 =17^2, 324 =18^2, 343 = 7^3, 361 =19^2, 400 =20^2, 441 =21^2, 484 =22^2, 512 = 8^3 =2^9, 529 =23^2, 576 =24^2, 625 =25^2 =5^4, 676 =26^2, 729 =27^2 = 9^3 =3^6, 784 =28^2, 841 =29^2, 900 =30^2, 961 =31^2, 1000 =10^3, 1024 =32^2 =4^5 =2^10, 1089 =33^2, 1156 =34^2, 1225 =35^2, 1296 =36^2 =6^4, 1331 =11^3, 1369 =37^2, 1444 =38^2, 1521 =39^2, 1600 =40^2, 1681 =41^2, 1728 =12^3, 1764 =42^2, 1849 =43^2, 1936 =44^2, 2025 =45^2, 2048 =2^11, 2116 =46^2, 2187 =3^7, 2197 =13^3, 2209 =47^2, 2304 =48^2, 2401 =49^2 =7^4, 2500 =50^2, 2601 =51^2, 2704 =52^2, 2744 =14^3, 2809 =53^2, 2916 =54^2, 3025 =55^2, 3125 =5^5, 3136 =56^2, 3249 =57^2, 3364 =58^2, 3375 =15^3, 3481 =59^2, 3600 =60^2, 3721 =61^2, 3844 =62^2, 3969 =63^2, 4096 =64^2 =16^3 =8^4 =4^6 =2^12, 4225 =65^2, 4356 =66^2, 4489 =67^2, 4624 =68^2, 4761 =69^2, 4900 =70^2, 4913 =17^3, 5041 =71^2, 5184 =72^2, 5329 =73^2, 5476 =74^2, 5625 =75^2, 5776 =76^2, 5832 =18^3, 5929 =77^2, 6084 =78^2, 6241 =79^2, 6400 =80^2, 6561 =81^2 =9^4 =3^8, 6724 =82^2, 6859 =19^3, 6889 =83^2, 7056 =84^2, 7225 =85^2, 7396 =86^2, 7569 =87^2, 7744 =88^2, 7776 =6^5, 7921 =89^2, 8000 =20^3, 8100 =90^2, 8192 =2^13, 8281 =91^2, 8464 =92^2, 8649 =93^2, 8836 =94^2, 9025 =95^2, 9216 =96^2, 9261 =21^3, 9409 =97^2, 9604 =98^2, 9801 =99^2, 10000 =100^2 =10^4, ...