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A300902
a(n) = n! / Product_{p prime < n}.
2
1, 1, 2, 3, 4, 20, 24, 168, 192, 1728, 17280, 190080, 207360, 2695680, 2903040, 43545600, 696729600, 11844403200, 12541132800, 238281523200, 250822656000, 5267275776000, 115880067072000, 2665241542656000, 2781121609728000, 69528040243200000, 1807729046323200000
OFFSET
0,3
COMMENTS
Sum_{n >= 0} 1/a(n) = 3.1868081118360746...
LINKS
FORMULA
a(n) = A000142(n)/A034386(n-1) for n>0, a(0) = 1.
a(n) = A049614(n)*A089026(n) for n>0, a(0) = 1.
EXAMPLE
a(6) = 6! / Product_{p prime < 6} = 6 * 5 * 4 * 3 * 2/(5 * 3 * 2) = 6 * 4 = 24.
MAPLE
a:= n-> n!/mul(`if`(isprime(i), i, 1), i=1..n-1):
seq(a(n), n=0..30); # Alois P. Heinz, Mar 16 2018
MATHEMATICA
Table[n!/(Times@@Prime[Range[PrimePi[n - 1]]]), {n, 0, 29}] (* Alonso del Arte, Mar 25 2018 *)
PROG
(PARI) a(n) = my(v=primes(primepi(n-1))); n!/prod(k=1, #v, v[k]); \\ Michel Marcus, Mar 15 2018
(Julia)
using Nemo
A300902(n) = div(fac(n), primorial(max(1, n-1)))
[A300902(n) for n in 0:26] |> println # Peter Luschny, Mar 16 2018
(Python)
from __future__ import division
from sympy import isprime
A300902_list, m = [1], 1
for n in range(1, 501):
m *= n
A300902_list.append(m)
if isprime(n):
m //= n # Chai Wah Wu, Mar 16 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Pedro Caceres, Mar 14 2018
STATUS
approved