phi(s(n^3)) is a square, where s(n) is sigma(n)-n (A001065).

Terms

a(0) =4a(1) =7a(2) =9a(3) =61a(4) =73a(5) =81a(6) =121a(7) =144a(8) =431a(9) =727a(10) =919a(11) =1596a(12) =2413a(13) =2593a(14) =2809a(15) =3966a(16) =6561a(17) =6827a(18) =9551a(19) =10593a(20) =12791a(21) =17053a(22) =29959a(23) =31238a(24) =33791a(25) =45115a(26) =47051a(27) =76157a(28) =79898a(29) =85607