A007467 Product of next n primes. (Formerly M2085)

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

Offset

1,1

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.

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)

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 *)

Prog

(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

Crossrefs

Cf. A139395, A139396, A238234.

Sequence in context: A179432 A007542 A090604 * A132317 A068409 A359849

Adjacent sequences: A007464 A007465 A007466 * A007468 A007469 A007470

Keyword

easy,nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

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

Status

approved