A255219 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.

1, 3, 14, 22, 31, 43, 46, 67, 71, 79, 94, 103, 118, 131, 139, 166, 191, 214, 223, 239, 283, 311, 334, 358, 367, 419, 422, 431, 439, 443, 454, 499, 526, 599, 607, 619, 643, 647, 659, 662, 683, 694, 718, 743, 766, 787, 823, 827, 907, 926, 934, 947, 958, 971, 1006

Offset

1,2

Comments

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).

Links

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

Example

31 is a term since mu(31) = -1 and mu(phi(31)) = mu(30) = -1.
7 is not a term since mu(7) = -1 and mu(phi(7)) = mu(6) = 1.
24 is not a term since mu(24) = 0 (i.e., 24 is not squarefree).

Mathematica

Select[Range[1000], Abs[MoebiusMu[#] + MoebiusMu[EulerPhi[#]]] == 2 &] (* Alonso del Arte, Feb 17 2015 *)

Prog

(Sage) [n for n in [1..1006] if moebius(n)==moebius(euler_phi(n)) if moebius(n)!=0]
(PARI) for(n=1, 1006, if(abs(moebius(n) + moebius(eulerphi(n))) == 2, print1(n, ", "))) \\ Indranil Ghosh, Mar 10 2017

Crossrefs

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

Sequence in context: A361909 A300216 A258218 * A226341 A024473 A024598

Adjacent sequences: A255216 A255217 A255218 * A255220 A255221 A255222

Keyword

nonn

Author

Tom Edgar, Feb 17 2015

Status

approved