A049199 Nonsquarefree numbers whose Euler totient function is also nonsquarefree.

8, 12, 16, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 68, 72, 75, 76, 80, 81, 84, 88, 90, 92, 96, 99, 100, 104, 108, 112, 116, 117, 120, 124, 125, 126, 128, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 169

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

Prime powers with sufficiently large exponents are in this sequence, including 8, 16, 32, 64, ..., 27, 81, ..., 25, 125.

Examples

			124 = 4*31 is in the sequence because phi(124)=60 and neither 124 nor 60 is squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A005117, A013929, A049198.

Programs

Mathematica

Select[Range[170], !SquareFreeQ[#] && !SquareFreeQ[EulerPhi[#]] &] (* Amiram Eldar, Jul 13 2019 *)

PARI

isok(n) = !issquarefree(n) && ! issquarefree(eulerphi(n)); \\ Michel Marcus, Jul 13 2019

Formula

k such that abs(mu(k)) = 0 and abs(mu(phi(k))) = 0.