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

Author

Wolfdieter Lang, May 10 2002

Keywords

• nonn
• easy

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

Also, odd numbers n for which sigma(n)*phi(n)/n^2 reaches a new record low, monotonically decreasing to the lower bound 8/Pi^2. - M. F. Hasler, Jul 08 2025

Links

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

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.

Programs

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 *)

PARI

a(n) = prod(k=2, n, prime(k)) \\ Michel Marcus, Mar 25 2017, simplified by M. F. Hasler, Jul 09 2025

Python

from sympy import primorial
def A070826(n): return primorial(n)>>1 # Chai Wah Wu, Jul 21 2022

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)

a(n) = A000040(n)*a(n-1) for n > 1, a(1) = 1. - M. F. Hasler, Jul 09 2025

Extensions

Formula corrected by Gary Detlefs, Dec 07 2011