A110423 a(n) = (n+1)(n+2)...(n+prime(k)) where prime(k) <= n < prime(k+1).

12, 120, 210, 30240, 55440, 17297280, 32432400, 57657600, 98017920, 28158588057600, 53970627110400, 64764752532480000, 124903451312640000, 233153109116928000, 422590010274432000, 830034394580628357120000

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..366

Formula

a(p) = (2p)!/p! if p is a prime.

a(n) = (n+A007917(n))!/n!. - Robert Israel, Aug 18 2019

Example

a(6) = 7*8*9*10*11 = 55440.

Maple

p:=proc(n) if isprime(n)=true then n else prevprime(n) fi end: a:=n->product(n+j, j=1..p(n)): seq(a(n), n=2..19); # p is a modified prevprime command (for n prime yields n rather than the previous prime) # Emeric Deutsch, Aug 07 2005
# Simpler alternative:
seq((n+prevprime(n+1))!/n!, n=2..20); # Robert Israel, Aug 18 2019

Mathematica

Table[Pochhammer[n+1, NextPrime[n+1, -1]], {n, 2, 20}] (* Jean-François Alcover, Jul 19 2020 *)

Crossrefs

Cf. A007917, A110424.

Sequence in context: A075366 A276668 A076633 * A006953 A164877 A121032

Adjacent sequences: A110420 A110421 A110422 * A110424 A110425 A110426

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 01 2005

Extensions

More terms from Emeric Deutsch, Aug 07 2005

Status

approved