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,
...