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%I #42 Apr 16 2023 15:55:28
%S 1,4,6,720,12,3360,18,9240,11793600,30,45239040,59280,42,91080,
%T 311875200,549853920,60,1072431360,328440,72,2533330800,531360,
%U 4701090240,60072730099200,970200,102,1157520,108,1367520,1063186156509747740870400000,2146560,43191973440
%N Product of composite numbers between the n-th and (n+1)st primes.
%H T. D. Noe, <a href="/A061214/b061214.txt">Table of n, a(n) for n = 1..2000</a>
%F A006530(a(n)) = A052248(n) for n > 1. - _Reinhard Zumkeller_, Jun 22 2011
%e 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.
%p A061214 := proc(n)
%p local k ;
%p product(k,k=ithprime(n)+1..ithprime(n+1)-1) ;
%p end proc: # _R. J. Mathar_, Apr 23 2013
%t Table[Times@@Range[Prime[n]+1,Prime[n+1]-1],{n,30}] (* _Harvey P. Dale_, Jun 14 2011 *)
%t Times@@Range[#[[1]]+1,#[[2]]-1]&/@Partition[Prime[Range[40]],2,1] (* _Harvey P. Dale_, Apr 23 2022 *)
%o (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
%o (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
%o (Haskell)
%o a061214 n = a061214_list !! (n-1)
%o a061214_list = f a000040_list where
%o f (p:ps'@(p':ps)) = (product [p+1..p'-1]) : f ps'
%o -- _Reinhard Zumkeller_, Jun 22 2011
%o (Python)
%o from math import prod
%o from sympy import prime
%o def A061214(n): return prod(i for i in range(prime(n)+1,prime(n+1))) # _Chai Wah Wu_, Jul 10 2022
%Y Cf. A006530, A052248, A052297, A072472, A361760, A361761.
%Y Cf. A046933 and A054265 (number and sum of these composites).
%K nonn
%O 1,2
%A _Amarnath Murthy_, Apr 21 2001
%E More terms from _James A. Sellers_, Apr 24 2001
%E Better definition from _T. D. Noe_, Jan 21 2008
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