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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.

%I A178705 #15 Sep 25 2020 05:39:26
%S A178705 49,91,121,133,169,175,217,231,247,259,301,325,341,343,361,385,403,
%T A178705 427,435,451,469,475,481,511,529,553,559,561,589,595,637,645,651,671,
%U A178705 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
%N 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.
%C A178705 Odd composite numbers q such that gcd(A000010(q), A000265(q-1)) > 1. - _Robert Israel_, Dec 20 2017
%H A178705 Robert Israel, <a href="/A178705/b178705.txt">Table of n, a(n) for n = 1..10000</a>
%F A178705 a^d == 1 mod q
%e A178705 18^3 == 1 mod 49
%p A178705 filter:= proc(n)
%p A178705   if isprime(n) then return false fi;
%p A178705   igcd((n-1)/2^padic:-ordp(n-1,2), numtheory:-phi(n)) > 1
%p A178705 end proc:
%p A178705 select(filter, [seq(i,i=9..2000,2)]); # _Robert Israel_, Dec 20 2017
%t A178705 filterQ[n_] := If[PrimeQ[n], False, GCD[(n-1)/2^IntegerExponent[n-1, 2], EulerPhi[n]] > 1];
%t A178705 Select[Range[9, 2000, 2], filterQ] (* _Jean-François Alcover_, Sep 25 2020, after _Robert Israel_ *)
%Y A178705 Cf. A000010, A000265.
%K A178705 nonn
%O A178705 1,1
%A A178705 _Karsten Meyer_, Dec 26 2010
%E A178705 Corrected by _Robert Israel_, Dec 20 2017