A061214 Product of composite numbers between the n-th and (n+1)st primes.

1, 4, 6, 720, 12, 3360, 18, 9240, 11793600, 30, 45239040, 59280, 42, 91080, 311875200, 549853920, 60, 1072431360, 328440, 72, 2533330800, 531360, 4701090240, 60072730099200, 970200, 102, 1157520, 108, 1367520, 1063186156509747740870400000, 2146560, 43191973440

Offset: 1

Author

Amarnath Murthy, Apr 21 2001

Keywords

• nonn

Examples

			a(4) = 8 * 9 * 10 = 720. 7 is the fourth prime and 11 is the fifth prime. a(5) = 12 as 11 and 13 both are primes.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A006530, A052248, A052297, A072472, A361760, A361761.

Cf. A046933 and A054265 (number and sum of these composites).

Programs

Haskell

a061214 n = a061214_list !! (n-1)
a061214_list = f a000040_list where
   f (p:ps'@(p':ps)) = (product [p+1..p'-1]) : f ps'
-- Reinhard Zumkeller, Jun 22 2011

Maple

A061214 := proc(n)
    local k ;
    product(k,k=ithprime(n)+1..ithprime(n+1)-1) ;
end proc: # R. J. Mathar, Apr 23 2013

Mathematica

Table[Times@@Range[Prime[n]+1,Prime[n+1]-1],{n,30}] (* Harvey P. Dale, Jun 14 2011 *)
Times@@Range[#[[1]]+1,#[[2]]-1]&/@Partition[Prime[Range[40]],2,1] (* Harvey P. Dale, Apr 23 2022 *)

PARI

{ n=0; q=2; forprime (p=3, prime(2001), a=1; for (i=q + 1, p - 1, a*=i); q=p; write("b061214.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 19 2009

PARI

v=primes(100);for(i=1,#v-1,v[i]=prod(j=v[i]+1,v[i+1]-1,j));vecextract(v,"1..-2") \\ Charles R Greathouse IV, Feb 27 2012

Python

from math import prod
from sympy import prime
def A061214(n): return prod(i for i in range(prime(n)+1,prime(n+1))) # Chai Wah Wu, Jul 10 2022

Formula

A006530(a(n)) = A052248(n) for n > 1. - Reinhard Zumkeller, Jun 22 2011

Extensions

More terms from James Sellers, Apr 24 2001

Better definition from T. D. Noe, Jan 21 2008