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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A005117, A013929, A049198.

Sequence in context: A063539 A253296 A081925 * A337806 A192544 A302139

Adjacent sequences: A049196 A049197 A049198 * A049200 A049201 A049202

Keyword

nonn

Author

Labos Elemer

Status

approved