A328665 Least super-Poulet number (A050217) with n distinct prime factors.

341, 294409, 9972894583, 1264022137981459, 14054662152215842621

Offset: 2

Author

Amiram Eldar, Oct 24 2019

Keywords

• nonn
• more

Comments

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

From Daniel Suteu, Oct 28 2019: (Start)

a(8) <= 192463418472849397730107809253922101,

a(9) <= 1347320741392600160214289343906212762456021,

a(10) <= 70865138168006643427403953978871929070133095474701,

a(11) <= 3363391752747838578311772729701478698952546288306688208857,

a(12) <= 132153369641266990823936945628293401491197666138621036175881960329,

a(13) <= 9105096650335639994239038954861714246150666715328403635257215036295306537. (End)

Links

• Gérard P. Michon, Super-pseudoprimes to Base a, Numericana, 2005.
• Eric Weisstein's World of Mathematics, Super-Poulet Numbers
• Wikipedia, Super-Poulet number

Crossrefs

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

Programs

Mathematica

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]

PARI

isok(k, n) = if (omega(k) == n, fordiv(k, d, if(Mod(2, d)^d!=2, return(0))); return(1));
a(n) = my(k=4); while (!isok(k, n), k++); k; \\ Michel Marcus, Oct 28 2019

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