Perfect (or pure) powers pp such that sigma(pp) is also a perfect (pure) power.

Terms

a(0) =1a(1) =81a(2) =343a(3) =400a(4) =32400a(5) =1705636a(6) =3648100a(7) =138156516a(8) =295496100a(9) =1055340196a(10) =1476326929a(11) =1857437604a(12) =2263475776a(13) =2323432804a(14) =2592846400a(15) =2661528100a(16) =7036525456a(17) =10994571025a(18) =17604513124a(19) =39415749156a(20) =61436066769a(21) =85482555876a(22) =90526367376a(23) =97577515876a(24) =98551417041