A049421 Composite numbers k such that k!/k# - 1 is prime, where k# = primorial numbers A034386.

4, 6, 8, 16, 21, 34, 39, 45, 50, 72, 76, 133, 164, 202, 216, 221, 280, 496, 605, 2532, 2967, 3337, 8711, 10977, 13724, 15250, 18160, 20943, 33684, 41400

Offset: 1

Author

Paul Jobling (paul.jobling(AT)whitecross.com)

Keywords

• hard
• nonn

Comments

k!/k# is known as n compositorial.

Subset of A140293. Prime numbers are excluded since k!/k# = (k-1)!/(k-1)# when k is prime. - Giovanni Resta, Mar 28 2013

a(31) > 50000. - Roger Karpin, Jul 08 2015

Links

• Chris Caldwell, Compositorial

Crossrefs

Cf. A034386, A140293, A140294, A140315, A049420, A057017.

Programs

Mathematica

Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
Select[Range[2,
1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) - 1] &] (* Robert Price, Oct 11 2019 *)

Extensions

More terms from Robert G. Wilson v, Jun 21 2001

a(23)-a(25) from Giovanni Resta, Apr 02 2013

a(26) from Roger Karpin, Nov 29 2014

a(27)-a(28) from Daniel Heuer, ca Aug 2000

a(29)-a(30) from Serge Batalov, Feb 09 2015