A039772 Even numbers k such that phi(k) and k-1 are distinct and have a common factor > 1.

28, 52, 66, 70, 76, 112, 124, 130, 148, 154, 172, 176, 186, 190, 196, 208, 232, 238, 244, 246, 268, 276, 280, 286, 292, 304, 310, 316, 322, 344, 364, 366, 370, 388, 396, 406, 412, 418, 426, 430, 436, 442, 448, 490, 496, 506, 508, 520, 532, 556, 568, 574

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Also this sequence is the union of all possible even Fermat pseudoprimes q to some prime base p>q such that q does not divide p-1. Note that all even nonprime divisors of p-1 are the Fermat pseudoprimes to prime base p. E.g. q = {4,6,12,18,28,36} is a set of even Fermat pseudoprimes to prime base p = 37, but only number q = 28 from this set does not divide p-1 = 36. - Alexander Adamchuk, Jun 16 2007

Examples

			phi(28)=12, gcd(12,27)=3.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Romeo Meštrović, Generalizations of Carmichael numbers I, arXiv:1305.1867v1 [math.NT], May 04 2013.
• Eric Weisstein's World of Mathematics, Fermat Pseudoprime

Crossrefs

Cf. A000010, A049559.

Programs

Maple

select(t -> igcd(numtheory:-phi(t), t-1)>1, [seq(n,n=2..1000,2)]); # Robert Israel, May 15 2017

Mathematica

Select[Range[2, 1000, 2], !CoprimeQ[EulerPhi[#], #-1]&] (* Jean-François Alcover, Sep 19 2018 *)

PARI

isok(n) = !(n%2) && (gcd(eulerphi(n), n-1) != 1); \\ Michel Marcus, Mar 15 2019