A178705 Odd composite numbers q such that there exists a, 2<=a<=q-2, such that a^d == 1 mod q where d = A000265(q-1). Thus q is a strong pseudoprime in base a.

49, 91, 121, 133, 169, 175, 217, 231, 247, 259, 301, 325, 341, 343, 361, 385, 403, 427, 435, 451, 469, 475, 481, 511, 529, 553, 559, 561, 589, 595, 637, 645, 651, 671, 679, 703, 715, 721, 763, 775, 781, 793, 805, 817, 841, 847, 861, 871, 889, 891, 925, 931, 949, 961, 973, 1001, 1015, 1027, 1035, 1045

Offset

1,1

Comments

Odd composite numbers q such that gcd(A000010(q), A000265(q-1)) > 1. - Robert Israel, Dec 20 2017

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a^d == 1 mod q

Example

18^3 == 1 mod 49

Maple

filter:= proc(n)
  if isprime(n) then return false fi;
  igcd((n-1)/2^padic:-ordp(n-1, 2), numtheory:-phi(n)) > 1
end proc:
select(filter, [seq(i, i=9..2000, 2)]); # Robert Israel, Dec 20 2017

Mathematica

filterQ[n_] := If[PrimeQ[n], False, GCD[(n-1)/2^IntegerExponent[n-1, 2], EulerPhi[n]] > 1];
Select[Range[9, 2000, 2], filterQ] (* Jean-François Alcover, Sep 25 2020, after Robert Israel *)

Crossrefs

Cf. A000010, A000265.

Sequence in context: A350704 A157342 A230226 * A118886 A198773 A320633

Adjacent sequences: A178702 A178703 A178704 * A178706 A178707 A178708

Keyword

nonn

Author

Karsten Meyer, Dec 26 2010

Extensions

Corrected by Robert Israel, Dec 20 2017

Status

approved