A196529 -id:A196529 - cp's OEIS frontend

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

Wolfdieter Lang, May 10 2002

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

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

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.

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

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 *)

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

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

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

Formula corrected by Gary Detlefs, Dec 07 2011

A196527 Greatest common divisor of sums of first n prime numbers and first n composite numbers.

Original entry on oeis.org

2, 5, 2, 1, 1, 1, 1, 1, 2, 1, 4, 1, 7, 1, 8, 1, 1, 1, 1, 1, 8, 7, 1, 1, 1, 3, 2, 1, 4, 3, 1, 1, 28, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 1, 26, 1, 2, 1, 1, 1, 2, 1, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 1, 1, 10, 1, 2, 1, 1, 1, 1, 3, 8

Offset: 1

Reinhard Zumkeller, Oct 03 2011

nonn

a(n) = gcd(A007504(n),A053767(n));

a(A196528(n)) = n and a(m) <> n for m < A196528(n).

			a(1) = gcd(2,4) = 2;
a(2) = gcd(2+3,4+6) = gcd(5,10) = 5;
a(3) = gcd(2+3+5,4+6+8) = gcd(10,18) = 2;
a(4) = gcd(2+3+5+7,4+6+8+9) = gcd(17,19) = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A196529.

Module[{nn=90,pr,cmp},pr=Accumulate[Prime[Range[nn]]];cmp=Accumulate[ Take[Select[Range[2nn],CompositeQ],nn]];GCD@@#&/@Thread[{pr,cmp}]] (* Harvey P. Dale, Jul 29 2017 *)

cp's OEIS Frontend

A070826 One half of product of first n primes A000040.

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