Numbers k such that sigma(k) and sigma(k+1) are nontrivial powers (A065496).

Terms

a(0) =21a(1) =93a(2) =381a(3) =1065a(4) =1173a(5) =5065a(6) =5670a(7) =5729a(8) =6603a(9) =8809a(10) =10281a(11) =10680a(12) =15960a(13) =17110a(14) =39286a(15) =40526a(16) =47882a(17) =49951a(18) =61962a(19) =85058a(20) =85261a(21) =99066a(22) =117860a(23) =125985a(24) =126853a(25) =135890a(26) =143241a(27) =159901a(28) =171945a(29) =179556