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

1,2

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

Links

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

Example

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.

Mathematica

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

Prog

(Sage)
[n for n in [1..1000] if moebius(n)==moebius(euler_phi(n))]
(PARI) for(n=1, 140, if(moebius(n) == moebius(eulerphi(n)), print1(n, ", "))) \\  Indranil Ghosh, Mar 11 2017

Crossrefs

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

Sequence in context: A288865 A331069 A161517 * A280239 A344345 A310284

Adjacent sequences: A255196 A255197 A255198 * A255200 A255201 A255202

Keyword

nonn

Author

Tom Edgar, Feb 16 2015

Status

approved