A178997 Super-Poulet numbers having more than two different prime factors.

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

Offset

1,1

Comments

This is a subsequence of the super-Poulet numbers, A050217. Of the first 1000 super-Poulet 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 Super-Poulet 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. Garcia-Pulgarin, 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. García-Pulgarín, J. M. Velásquez-Soto 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]] (* Jean-François 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: A328935 A335584 A182206 * A328938 A291637 A206237

Adjacent sequences: A178994 A178995 A178996 * A178998 A178999 A179000

Keyword

nonn

Author

T. D. Noe, Jan 11 2011

Status

approved