A117307 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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