A049195 Numbers k such that the Euler totient function phi(k) is divisible by a square.

5, 8, 10, 12, 13, 15, 16, 17, 19, 20, 21, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 44, 45, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95

Offset

1,1

Comments

For k > 2 and p a prime: p^k is in this sequence. - Enrique Pérez Herrero, Apr 25 2013

The asymptotic density of this sequence is 1 since its complement (A049149) has a density 0. - Amiram Eldar, Mar 02 2021

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..2500

Example

72 and 73 belong because neither phi(72) = 24 nor phi(73) = 72 are squarefree.

Mathematica

Select[Range[100], MoebiusMu[EulerPhi[#]] == 0 &]
Select[Range[100], !SquareFreeQ[EulerPhi[#]]&] (* Harvey P. Dale, Apr 30 2018 *)

Crossrefs

Complement of A049149.

Cf. A000010, A005117, A013929.

Sequence in context: A205841 A344443 A332556 * A172019 A064362 A173298

Adjacent sequences: A049192 A049193 A049194 * A049196 A049197 A049198

Keyword

nonn

Author

Labos Elemer

Status

approved