A255199 - OEIS

%I #25 Apr 04 2021 00:50:28

%S 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 56,60,63,64,67,68,71,72,75,76,79,80,81,84,88,90,92,94,96,99,100,103,

%U 104,108,112,116,117,118,120,124,125,126,128,131,132,135,136,139

%N 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 If k and phi(k) are both not squarefree then k is in the list.

%C A prime p is in the list if p - 1 is squarefree and bigomega(p - 1) = A001222(p - 1) is odd.

%C It follows that the subsequence of primes is A078330. - _Bernard Schott_, Apr 03 2021

%H Amiram Eldar, <a href="/A255199/b255199.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 is in the list since mu(8) = 0 and mu(phi(8)) = mu(4) = 0.

%e 7 is not in the list since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.

%t Select[Range[200], MoebiusMu[#] == MoebiusMu[EulerPhi[#]] &] (* _Alonso del Arte_, Feb 16 2015 *)

%o (Sage)

%o [n for n in [1..1000] if moebius(n)==moebius(euler_phi(n))]

%o (PARI) for(n=1, 140, if(moebius(n) == moebius(eulerphi(n)), print1(n,", "))) \\  _Indranil Ghosh_, Mar 11 2017

%Y Cf. A000010, A008683, A033631, A013929, A078330.

%K nonn

%O 1,2

%A _Tom Edgar_, Feb 16 2015