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A178997 Super-Poulet 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 (list; graph; refs; listen; history; text; internal format)
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: 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

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)