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A300902 a(n) = n! / Product_{p prime < n}.

%I A300902 #66 Apr 09 2018 03:00:05
%S A300902 1,1,2,3,4,20,24,168,192,1728,17280,190080,207360,2695680,2903040,
%T A300902 43545600,696729600,11844403200,12541132800,238281523200,250822656000,
%U A300902 5267275776000,115880067072000,2665241542656000,2781121609728000,69528040243200000,1807729046323200000
%N A300902 a(n) = n! / Product_{p prime < n}.
%C A300902 Sum_{n >= 0} 1/a(n) = 3.1868081118360746...
%H A300902 Chai Wah Wu, <a href="/A300902/b300902.txt">Table of n, a(n) for n = 0..500</a>
%F A300902 a(n) = A000142(n)/A034386(n-1) for n>0, a(0) = 1.
%F A300902 a(n) = A049614(n)*A089026(n) for n>0, a(0) = 1.
%e A300902 a(6) = 6! / Product_{p prime < 6} = 6 * 5 * 4 * 3 * 2/(5 * 3 * 2) = 6 * 4 = 24.
%p A300902 a:= n-> n!/mul(`if`(isprime(i), i, 1), i=1..n-1):
%p A300902 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 16 2018
%t A300902 Table[n!/(Times@@Prime[Range[PrimePi[n - 1]]]), {n, 0, 29}] (* _Alonso del Arte_, Mar 25 2018 *)
%o A300902 (PARI) a(n) = my(v=primes(primepi(n-1))); n!/prod(k=1, #v, v[k]); \\ _Michel Marcus_, Mar 15 2018
%o A300902 (Julia)
%o A300902 using Nemo
%o A300902 A300902(n) = div(fac(n), primorial(max(1, n-1)))
%o A300902 [A300902(n) for n in 0:26] |> println # _Peter Luschny_, Mar 16 2018
%o A300902 (Python)
%o A300902 from __future__ import division
%o A300902 from sympy import isprime
%o A300902 A300902_list, m = [1], 1
%o A300902 for n in range(1,501):
%o A300902     m *= n
%o A300902     A300902_list.append(m)
%o A300902     if isprime(n):
%o A300902         m //= n # _Chai Wah Wu_, Mar 16 2018
%Y A300902 Cf. A000142, A034386, A049614, A066332, A089026.
%K A300902 nonn
%O A300902 0,3
%A A300902 _Pedro Caceres_, Mar 14 2018