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

Author

Tom Edgar, Feb 17 2015

Keywords

• nonn

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).

Examples

			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).
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

for(n=1, 1006, if(abs(moebius(n) + moebius(eulerphi(n))) == 2, print1(n,", "))) \\ Indranil Ghosh, Mar 10 2017

Sage

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