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Nonsquarefree numbers whose Euler totient function is also nonsquarefree.
3

%I #14 Jul 13 2019 03:43:25

%S 8,12,16,20,24,25,27,28,32,36,40,44,45,48,50,52,54,56,60,63,64,68,72,

%T 75,76,80,81,84,88,90,92,96,99,100,104,108,112,116,117,120,124,125,

%U 126,128,132,135,136,140,144,147,148,150,152,153,156,160,162,164,168,169

%N Nonsquarefree numbers whose Euler totient function is also nonsquarefree.

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

%H Amiram Eldar, <a href="/A049199/b049199.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t Select[Range[170], !SquareFreeQ[#] && !SquareFreeQ[EulerPhi[#]] &] (* _Amiram Eldar_, Jul 13 2019 *)

%o (PARI) isok(n) = !issquarefree(n) && ! issquarefree(eulerphi(n)); \\ _Michel Marcus_, Jul 13 2019

%Y Cf. A000010, A005117, A013929, A049198.

%K nonn

%O 1,1

%A _Labos Elemer_