%I
%S 294409,1398101,1549411,1840357,12599233,13421773,15162941,15732721,
%T 28717483,29593159,61377109,66384121,67763803,74658629,78526729,
%U 90341197,96916279,109322501
%N SuperPoulet numbers having more than two different prime factors.
%C This is a subsequence of the superPoulet numbers, A050217. Of the first 1000 superPoulet numbers, only 18 have more than two prime factors.
%C a(10000) = A001567(5287334), so about 0.19% of the pseudoprimes in that range are in this sequence.  _Charles R Greathouse IV_, Sep 16 2016
%C The smallest SuperPoulet number with three prime factors not all distinct is 5654273717 = 4733*1093^2, which is not in this sequence.  _Emmanuel Vantieghem_, Sep 25 2018
%H Charles R Greathouse IV, <a href="/A178997/b178997.txt">Table of n, a(n) for n = 1..10000</a>
%H V. Shevelev, G. GarciaPulgarin, J. M. Velasquez and J. H. Castillo, <a href="http://arxiv.org/abs/1206.0606">Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers</a>, arXiv preprint arXiv:1206:0606 [math.NT], 2012.  From _N. J. A. Sloane_, Oct 28 2012
%H V. Shevelev, G. GarcíaPulgarín, J. M. VelásquezSoto and J. H. Castillo, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Castillo/castillo2.html">Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers</a>, J. Integer Seq. 15 (2012) Article 12.7.7.
%t okQ[n_] := CompositeQ[n] && PrimeNu[n] > 2 && AllTrue[Divisors[n], PowerMod[2, #, n] == 2&];
%t Reap[For[n = 1, n < 10^8, n = n+2, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* _JeanFrançois Alcover_, Sep 11 2018 *) (* Corrected with PrimeNu instead of PrimeOmega by _Emmanuel Vantieghem_, Sep 24 2018 *)
%o (PARI) is(n)=my(f=factor(n)); if(#f~ < 3, return(0)); fordiv(f, d, if(Mod(2, d)^d!=2, return(0))); 1 \\ _Charles R Greathouse IV_, Sep 01 2016
%K nonn,more
%O 1,1
%A _T. D. Noe_, Jan 11 2011
