A070826 One half of product of first n primes A000040.

1, 3, 15, 105, 1155, 15015, 255255, 4849845, 111546435, 3234846615, 100280245065, 3710369067405, 152125131763605, 6541380665835015, 307444891294245705, 16294579238595022365, 961380175077106319535, 58644190679703485491635, 3929160775540133527939545, 278970415063349480483707695

Offset

1,2

Comments

Also, with offset 0, product of first n odd primes. - N. J. A. Sloane, Feb 26 2017

Identical to A002110(n)/2, n>=1.

a(n+1) is the least odd number with exactly n distinct prime divisors. - Labos Elemer, Mar 24 2003

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n) = A002110(n)/2.

From Antti Karttunen, Feb 06 2024: (Start)

a(1) = 1, and for n > 1, a(n) = A276086(A060389(n-1)).

a(n) = A024451(n) - 2*A203008(n-1).

(End)

Maple

a:=n->mul(ithprime(j), j=2..n):seq(a(n), n=1..17); # Zerinvary Lajos, Aug 24 2008

Mathematica

Rest[ FoldList[ Times, 1, Prime[ Range[ 18]] ]]/2 (* Robert G. Wilson v, Feb 17 2004 *)
FoldList[Times, 1, Prime[Range[2, 18]]] (* Zak Seidov, Jan 26 2009 *)

Prog

(PARI) a(n) = prod(k=1, n, prime(k))/2; \\ Michel Marcus, Mar 25 2017
(Python)
from sympy import primorial
def A070826(n): return primorial(n)>>1 # Chai Wah Wu, Jul 21 2022

Crossrefs

Cf. A003266 (for Fibonacci), A070825 (for Lucas), A003046 (for Catalan).

Cf. also A002110, A024451, A060389, A091852, A276086, A203008 [= A003415(a(1+n))].

Range of A196529.

Sequence in context: A207818 A354218 A118750 * A048599 A129731 A269455

Adjacent sequences: A070823 A070824 A070825 * A070827 A070828 A070829

Keyword

nonn,easy

Author

Wolfdieter Lang, May 10 2002

Extensions

Formula corrected by Gary Detlefs, Dec 07 2011

Status

approved