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Numbers k such that the Euler totient function phi(k) is divisible by a square.
3

%I #18 Mar 02 2021 05:59:37

%S 5,8,10,12,13,15,16,17,19,20,21,24,25,26,27,28,29,30,32,33,34,35,36,

%T 37,38,39,40,41,42,44,45,48,50,51,52,53,54,55,56,57,58,60,61,63,64,65,

%U 66,68,69,70,72,73,74,75,76,77,78,80,81,82,84,85,87,88,89,90,91,92,93,95

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

%C For k > 2 and p a prime: p^k is in this sequence. - _Enrique Pérez Herrero_, Apr 25 2013

%C The asymptotic density of this sequence is 1 since its complement (A049149) has a density 0. - _Amiram Eldar_, Mar 02 2021

%H Enrique Pérez Herrero, <a href="/A049195/b049195.txt">Table of n, a(n) for n = 1..2500</a>

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

%t Select[Range[100], MoebiusMu[EulerPhi[#]] == 0 &]

%t Select[Range[100],!SquareFreeQ[EulerPhi[#]]&] (* _Harvey P. Dale_, Apr 30 2018 *)

%Y Complement of A049149.

%Y Cf. A000010, A005117, A013929.

%K nonn

%O 1,1

%A _Labos Elemer_