Numbers k such that both k and sigma(k)=A000203(k) are powerful, i.e., are terms of A001694.

Terms

a(0) =1a(1) =81a(2) =343a(3) =400a(4) =9261a(5) =27783a(6) =32400a(7) =137200a(8) =189728a(9) =224939a(10) =972000a(11) =1705636a(12) =2205472a(13) =3087000a(14) =3591200a(15) =3648100a(16) =3704400a(17) =7968032a(18) =11113200a(19) =13645088a(20) =15350724a(21) =15367968a(22) =18220059a(23) =21161304a(24) =24240600a(25) =25992000a(26) =26680500a(27) =29184800a(28) =32832900a(29) =48586824