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

1,2

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002384.

Sequence in context: A117595 A050050 A222801 * A340877 A161890 A089388

Adjacent sequences: A117304 A117305 A117306 * A117308 A117309 A117310

Keyword

nonn

Author

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

Extensions

Corrected by Michel Marcus, Jun 01 2013

Status

approved