

A178997


SuperPoulet numbers having more than two different prime factors.


7



294409, 1398101, 1549411, 1840357, 12599233, 13421773, 15162941, 15732721, 28717483, 29593159, 61377109, 66384121, 67763803, 74658629, 78526729, 90341197, 96916279, 109322501
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OFFSET

1,1


COMMENTS

This is a subsequence of the superPoulet numbers, A050217. Of the first 1000 superPoulet numbers, only 18 have more than two prime factors.
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
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


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
V. Shevelev, G. GarciaPulgarin, J. M. Velasquez and J. H. Castillo, Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers, arXiv preprint arXiv:1206:0606 [math.NT], 2012.  From N. J. A. Sloane, Oct 28 2012
V. Shevelev, G. GarcíaPulgarín, J. M. VelásquezSoto and J. H. Castillo, Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers, J. Integer Seq. 15 (2012) Article 12.7.7.


MATHEMATICA

okQ[n_] := CompositeQ[n] && PrimeNu[n] > 2 && AllTrue[Divisors[n], PowerMod[2, #, n] == 2&];
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 *)


PROG

(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


CROSSREFS

Sequence in context: A328664 A328935 A182206 * A328938 A291637 A206237
Adjacent sequences: A178994 A178995 A178996 * A178998 A178999 A179000


KEYWORD

nonn,more


AUTHOR

T. D. Noe, Jan 11 2011


STATUS

approved



