A117307 Numbers for which (phi(n))^2+phi(n)+1 is a prime number.

1, 2, 3, 4, 6, 7, 9, 13, 14, 15, 16, 18, 20, 21, 24, 25, 26, 28, 30, 33, 35, 36, 39, 42, 44, 45, 50, 52, 56, 66, 67, 70, 72, 78, 79, 81, 84, 90, 121, 123, 134, 139, 151, 158, 162, 163, 164, 165, 176, 193, 200, 203, 215, 220, 221, 242, 243, 245, 246, 249

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 24 2006

Keywords

• nonn

Examples

			14 is in the sequence because (phi(14))^2+phi(14)+1 = 6^2+6+1 = 43, which is a prime number.
		

Links

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

Crossrefs

Cf. A000010, A002384.

Programs

Mathematica

f[x_] := x^2 + x + 1; Select[Range[250], PrimeQ[f[EulerPhi[#]]] &] (* Amiram Eldar, Feb 08 2021 *)

PARI

lista(nn) = {for (n = 1, nn, if (isprime((eulerphi(n))^2 + eulerphi(n) + 1), print1(n, ", ")););} \\ Michel Marcus, Jun 01 2013

Extensions

Corrected by Michel Marcus, Jun 01 2013