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

1,1

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.

Links

Table of n, a(n) for n=1..77.

Mathematica

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

Prog

(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

Crossrefs

Cf. A111305, A181780, A209211.

Sequence in context: A102554 A371862 A070810 * A129930 A128510 A109289

Adjacent sequences: A227177 A227178 A227179 * A227181 A227182 A227183

Keyword

nonn

Author

Emmanuel Vantieghem, Jul 03 2013

Status

approved