A227180 Composite numbers n such that b^(n-1) == 1 (mod n) implies b == -1 or +1 (mod n).

4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 54, 56, 58, 60, 62, 64, 68, 72, 74, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 114, 116, 118, 120, 122, 126, 128, 132, 134, 136, 138, 140, 142, 144, 146, 150, 152, 156, 158, 160, 162, 164, 166, 168, 170

Offset: 1

Author

Emmanuel Vantieghem, Jul 03 2013

Keywords

• nonn

Comments

The sequence is the union of A111305 with {3^k | k > 1}.

The composite numbers not in this sequence are the Fermat pseudoprimes A181780.

Crossrefs

Cf. A111305, A181780, A209211.

Programs

Mathematica

FQ[k_]:= Block[{},GCD[EulerPhi[k],k-1]==1||IntegerQ[Log[3,k]]];Select[Range[4,170],FQ]

PARI

is(n)=for(b=2, n-2, if(Mod(b, n)^(n-1)==1, return(0))); !isprime(n) \\ Charles R Greathouse IV, Dec 22 2016