login
Least super-Poulet number (A050217) with n distinct prime factors.
1

%I #16 Oct 28 2019 18:24:30

%S 341,294409,9972894583,1264022137981459,14054662152215842621

%N Least super-Poulet number (A050217) with n distinct prime factors.

%C a(7) <= 1842158622953082708177091, and a(8) <= 317565023788749598474704753433331761 (from Michon's site).

%C From _Daniel Suteu_, Oct 28 2019: (Start)

%C a(8) <= 192463418472849397730107809253922101,

%C a(9) <= 1347320741392600160214289343906212762456021,

%C a(10) <= 70865138168006643427403953978871929070133095474701,

%C a(11) <= 3363391752747838578311772729701478698952546288306688208857,

%C a(12) <= 132153369641266990823936945628293401491197666138621036175881960329,

%C a(13) <= 9105096650335639994239038954861714246150666715328403635257215036295306537. (End)

%H GĂ©rard P. Michon, <a href="http://www.numericana.com/answer/pseudo.htm#super">Super-pseudoprimes to Base a</a>, Numericana, 2005.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Super-PouletNumber.html">Super-Poulet Numbers</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Super-Poulet_number">Super-Poulet number</a>

%t a[n_] := Module[{k=1}, While[PrimeNu[k] < n || PowerMod[2, k - 1, k] != 1 || Union @ PowerMod[2, Rest[Divisors[k]], k] != {2}, k++]; k]; Array[a, 3, 2]

%o (PARI) isok(k, n) = if (omega(k) == n, fordiv(k, d, if(Mod(2, d)^d!=2, return(0))); return(1));

%o a(n) = my(k=4); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Oct 28 2019

%o (PARI) isupperbound(n,k) = my(f=factor(k)); omega(f) == n && Mod(2, k)^gcd(vector(#f~, i, f[i,1]-1)) == 1; \\ _Daniel Suteu_, Oct 28 2019

%Y Cf. A001567, A007011, A050217, A178997, A300327.

%K nonn,more

%O 2,1

%A _Amiram Eldar_, Oct 24 2019