A007467 Product of next n primes.

2, 15, 1001, 215441, 95041567, 66238993967, 63009974049301, 87796770491685553, 173955570033393401009, 421385360593324054690769, 1172248885422611971256631487, 5253333091597988325086927419397, 21476254926032216698855019795863013

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• easy
• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..185
• Ronald K. Hoeflin, Titan Test.

Crossrefs

Cf. A139395, A139396, A238234.

Programs

Mathematica

terms=20;With[{prs=Prime[Range[(terms(terms+1))/2]]},Table[ Times@@ Take[prs,{(n(n-1))/2+1,(n(n+1))/2}],{n,terms}]] (* Harvey P. Dale, Aug 06 2013 *)
With[{nn=40},Times@@@TakeList[Prime[Range[(nn(nn+1))/2]],Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 15 2020 *)

PARI

a(n)=my(s=1);forprime(p=prime(n*(n-1)/2+1),prime(n*(n+1)/2),s*=p);s \\ Charles R Greathouse IV, Aug 06 2013

Python

from math import prod
from sympy import prime
def a(n): return prod(prime(i) for i in range((n-1)*n//2+1, n*(n+1)//2+1))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Feb 15 2021

Formula

From Amiram Eldar, Nov 15 2020: (Start)

Sum_{n>=1} 1/a(n) = A139395.

Sum_{n>=1} (-1)^(n+1)/a(n) = A238234 = 1 - A139396. (End)

Extensions

Corrected and extended by Harvey P. Dale, Aug 06 2013