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

Author

T. D. Noe, Jan 11 2011

Keywords

• nonn

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.

Programs

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 *)

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