A067583 Integers of the form phi(n^n)/phi(n)^n where phi is the Euler totient function A000010(n).

1, 2, 8, 243, 128, 177147, 32768, 129140163, 94143178827, 2147483648, 50031545098999707, 26588814358957503287787, 19383245667680019896796723, 9223372036854775808, 7509466514979724803946715958257547

Offset: 1

Author

Benoit Cloitre, Jan 30 2002

Keywords

• nonn

Programs

Mathematica

Select[Table[EulerPhi[n^n]/EulerPhi[n]^n,{n,100}],IntegerQ] (* Harvey P. Dale, Dec 19 2021 *)

Formula

If A007694(n)==0 (mod 3) (or equivalently if A007694(n) = 2^u*3^v with u, v >=1) then a(n) =3^(A007694(n) -1); if A007694(n)=2^u a(n)=2^(A007694(n) -1). Remark : if n=3^v phi(n^n)/phi(n)^n=1/2^(n-1)