A255219 - OEIS

%I #37 Mar 10 2024 04:02:05

%S 1,3,14,22,31,43,46,67,71,79,94,103,118,131,139,166,191,214,223,239,

%T 283,311,334,358,367,419,422,431,439,443,454,499,526,599,607,619,643,

%U 647,659,662,683,694,718,743,766,787,823,827,907,926,934,947,958,971,1006

%N Squarefree 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 A prime p is a term in the sequence if p - 1 is squarefree and bigomega(p - 1) = A001222(p - 1) is odd (see A078330).

%H Amiram Eldar, <a href="/A255219/b255219.txt">Table of n, a(n) for n = 1..10000</a>

%e 31 is a term since mu(31) = -1 and mu(phi(31)) = mu(30) = -1.

%e 7 is not a term since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.

%e 24 is not a term since mu(24) = 0 (i.e., 24 is not squarefree).

%t Select[Range[1000], Abs[MoebiusMu[#] + MoebiusMu[EulerPhi[#]]] == 2 &] (* _Alonso del Arte_, Feb 17 2015 *)

%o (Sage) [n for n in [1..1006] if moebius(n)==moebius(euler_phi(n)) if moebius(n)!=0]

%o (PARI) for(n=1, 1006, if(abs(moebius(n) + moebius(eulerphi(n))) == 2, print1(n,", "))) \\ _Indranil Ghosh_, Mar 10 2017

%Y Cf. A000010, A001222, A005117, A008683, A033631, A078330, A255199.

%K nonn

%O 1,2

%A _Tom Edgar_, Feb 17 2015