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.

1, 3, 8, 12, 14, 16, 20, 22, 24, 25, 27, 28, 31, 32, 36, 40, 43, 44, 45, 46, 48, 50, 52, 54, 56, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 81, 84, 88, 90, 92, 94, 96, 99, 100, 103, 104, 108, 112, 116, 117, 118, 120, 124, 125, 126, 128, 131, 132, 135, 136, 139

Offset: 1

Author

Tom Edgar, Feb 16 2015

Keywords

• nonn

Comments

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

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

It follows that the subsequence of primes is A078330. - Bernard Schott, Apr 03 2021

Examples

			8 is in the list since mu(8) = 0 and mu(phi(8)) = mu(4) = 0.
7 is not in the list since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

Select[Range[200], MoebiusMu[#] == MoebiusMu[EulerPhi[#]] &] (* Alonso del Arte, Feb 16 2015 *)

PARI

for(n=1, 140, if(moebius(n) == moebius(eulerphi(n)), print1(n,", "))) \\  Indranil Ghosh, Mar 11 2017

Sage

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