A066071 Nonprime numbers k such that phi(k) + 1 is prime.

1, 4, 6, 8, 9, 10, 12, 14, 18, 21, 22, 26, 27, 28, 32, 34, 36, 38, 40, 42, 46, 48, 49, 54, 55, 57, 58, 60, 62, 63, 74, 75, 76, 77, 82, 86, 88, 91, 93, 94, 95, 98, 99, 100, 106, 108, 110, 111, 114, 115, 117, 118, 119, 122, 124, 125, 126, 132, 133, 134, 135, 142, 145, 146

Offset: 1

Author

Labos Elemer, Dec 03 2001

Keywords

• nonn

Comments

A039698 with the primes removed. For every prime p, 2p is in the sequence. - Ray Chandler, May 26 2008

Includes 3*p for p in A005382 and p^2 for p in A065508. - Robert Israel, Dec 29 2017

Examples

			Solutions to 1+phi(x)=13 are {13, 21, 26, 28, 36, 42} of which the 5 composites are in the sequence.
		

Links

• Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A000010, A000040, A005382, A006093, A039649, A039698, A058339, A058340, A065508, A066072, A066073, A066074, A066075, A066076, A066077, A066080.

Programs

Magma

[n: n in [1..200] |not IsPrime(n) and IsPrime(EulerPhi(n)+1)]; // Vincenzo Librandi, Jul 02 2016

Maple

select(n -> not isprime(n) and isprime(1+numtheory:-phi(n)), [$1..1000]); # Robert Israel, Dec 29 2017

Mathematica

Select[Complement[Range@ #, Prime@ Range@ PrimePi@ #] &@ 150, PrimeQ[EulerPhi@ # + 1] &] (* Michael De Vlieger, Jul 01 2016 *)

PARI

isok(k) = { !isprime(k) && isprime(eulerphi(k) + 1) } \\ Harry J. Smith, Nov 10 2009