cp's OEIS Frontend

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

%I A049421 #27 Aug 12 2024 13:08:00
%S A049421 4,6,8,16,21,34,39,45,50,72,76,133,164,202,216,221,280,496,605,2532,
%T A049421 2967,3337,8711,10977,13724,15250,18160,20943,33684,41400
%N A049421 Composite numbers k such that k!/k# - 1 is prime, where k# = primorial numbers A034386.
%C A049421 k!/k# is known as n compositorial.
%C A049421 Subset of A140293. Prime numbers are excluded since k!/k# = (k-1)!/(k-1)# when k is prime. - _Giovanni Resta_, Mar 28 2013
%C A049421 a(31) > 50000. - _Roger Karpin_, Jul 08 2015
%H A049421 Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Compositorial">Compositorial</a>
%t A049421 Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
%t A049421 Select[Range[2,
%t A049421 1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) - 1] &] (* _Robert Price_, Oct 11 2019 *)
%Y A049421 Cf. A034386, A140293, A140294, A140315, A049420, A057017.
%K A049421 hard,nonn
%O A049421 1,1
%A A049421 Paul Jobling (paul.jobling(AT)whitecross.com)
%E A049421 More terms from _Robert G. Wilson v_, Jun 21 2001
%E A049421 a(23)-a(25) from _Giovanni Resta_, Apr 02 2013
%E A049421 a(26) from _Roger Karpin_, Nov 29 2014
%E A049421 a(27)-a(28) from Daniel Heuer, ca Aug 2000
%E A049421 a(29)-a(30) from _Serge Batalov_, Feb 09 2015