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

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

Author

Pedro Caceres, Mar 14 2018

Keywords

• nonn

Comments

Sum_{n >= 0} 1/a(n) = 3.1868081118360746...

Examples

			a(6) = 6! / Product_{p prime < 6} = 6 * 5 * 4 * 3 * 2/(5 * 3 * 2) = 6 * 4 = 24.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A034386, A049614, A066332, A089026.

Programs

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

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 *)

PARI

a(n) = my(v=primes(primepi(n-1))); n!/prod(k=1, #v, v[k]); \\ Michel Marcus, Mar 15 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

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.