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A255199 Numbers k such that mu(k) = mu(phi(k)) where mu(k) is the Möbius function and phi(k) is Euler's totient function.

%I A255199 #25 Apr 04 2021 00:50:28
%S A255199 1,3,8,12,14,16,20,22,24,25,27,28,31,32,36,40,43,44,45,46,48,50,52,54,
%T A255199 56,60,63,64,67,68,71,72,75,76,79,80,81,84,88,90,92,94,96,99,100,103,
%U A255199 104,108,112,116,117,118,120,124,125,126,128,131,132,135,136,139
%N A255199 Numbers k such that mu(k) = mu(phi(k)) where mu(k) is the Möbius function and phi(k) is Euler's totient function.
%C A255199 If k and phi(k) are both not squarefree then k is in the list.
%C A255199 A prime p is in the list if p - 1 is squarefree and bigomega(p - 1) = A001222(p - 1) is odd.
%C A255199 It follows that the subsequence of primes is A078330. - _Bernard Schott_, Apr 03 2021
%H A255199 Amiram Eldar, <a href="/A255199/b255199.txt">Table of n, a(n) for n = 1..10000</a>
%e A255199 8 is in the list since mu(8) = 0 and mu(phi(8)) = mu(4) = 0.
%e A255199 7 is not in the list since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.
%t A255199 Select[Range[200], MoebiusMu[#] == MoebiusMu[EulerPhi[#]] &] (* _Alonso del Arte_, Feb 16 2015 *)
%o A255199 (Sage)
%o A255199 [n for n in [1..1000] if moebius(n)==moebius(euler_phi(n))]
%o A255199 (PARI) for(n=1, 140, if(moebius(n) == moebius(eulerphi(n)), print1(n,", "))) \\  _Indranil Ghosh_, Mar 11 2017
%Y A255199 Cf. A000010, A008683, A033631, A013929, A078330.
%K A255199 nonn
%O A255199 1,2
%A A255199 _Tom Edgar_, Feb 16 2015