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%I #24 Apr 03 2023 10:36:09
%S 4,6,8,16,21,34,39,45,50,72,76,133,164,202,216,221,280,496,605,2532,
%T 2967,3337,8711,10977,13724,15250,18160,20943,33684,41400
%N Composite numbers n such that (n!/n#)-1 is prime, where n# = primorial numbers A034386.
%C n!/n# is known as n compositorial.
%C Subset of A140293. Prime numbers are excluded since n!/n# = (n-1)!/(n-1)# when n is prime. - _Giovanni Resta_, Mar 28 2013
%C a(31) > 50000. - _Roger Karpin_, Jul 08 2015
%H Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=Compositorial">Compositorial</a>
%t Primorial[n_] := Product[Prime[i], {i, 1, PrimePi[n]}];
%t Select[Range[2,
%t 1000], ! PrimeQ[#] && PrimeQ[(#! / Primorial[#]) - 1] &] (* _Robert Price_, Oct 11 2019 *)
%Y Cf. A034386, A140293, A140294, A140315, A049420.
%K hard,nonn
%O 1,1
%A Paul Jobling (paul.jobling(AT)whitecross.com)
%E More terms from _Robert G. Wilson v_, Jun 21 2001
%E a(23)-a(25) from _Giovanni Resta_, Apr 02 2013
%E a(26) from _Roger Karpin_, Nov 29 2014
%E a(27)-a(28) from Daniel Heuer, ca Aug 2000
%E a(29)-a(30) from _Serge Batalov_, Feb 09 2015
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