

A039772


Even numbers k such that phi(k) and k1 are distinct and have a common factor > 1.


8



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
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OFFSET

1,1


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 p1. Note that all even nonprime divisors of p1 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 p1 = 36.  Alexander Adamchuk, Jun 16 2007


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


EXAMPLE

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


MAPLE

select(t > igcd(numtheory:phi(t), t1)>1, [seq(n, n=2..1000, 2)]); # Robert Israel, May 15 2017


MATHEMATICA

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


PROG

(PARI) isok(n) = !(n%2) && (gcd(eulerphi(n), n1) != 1); \\ Michel Marcus, Mar 15 2019


CROSSREFS

Cf. A000010, A049559.
Sequence in context: A063770 A161923 A309145 * A291855 A181792 A181793
Adjacent sequences: A039769 A039770 A039771 * A039773 A039774 A039775


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



