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One half of product of first n primes A000040.
84

%I #46 Feb 08 2024 20:44:20

%S 1,3,15,105,1155,15015,255255,4849845,111546435,3234846615,

%T 100280245065,3710369067405,152125131763605,6541380665835015,

%U 307444891294245705,16294579238595022365,961380175077106319535,58644190679703485491635,3929160775540133527939545,278970415063349480483707695

%N One half of product of first n primes A000040.

%C Also, with offset 0, product of first n odd primes. - _N. J. A. Sloane_, Feb 26 2017

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

%C a(n+1) is the least odd number with exactly n distinct prime divisors. - _Labos Elemer_, Mar 24 2003

%H Vincenzo Librandi, <a href="/A070826/b070826.txt">Table of n, a(n) for n = 1..200</a>

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

%F From _Antti Karttunen_, Feb 06 2024: (Start)

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

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

%F (End)

%p a:=n->mul(ithprime(j), j=2..n):seq(a(n), n=1..17); # _Zerinvary Lajos_, Aug 24 2008

%t Rest[ FoldList[ Times, 1, Prime[ Range[ 18]] ]]/2 (* _Robert G. Wilson v_, Feb 17 2004 *)

%t FoldList[Times, 1, Prime[Range[2, 18]]] (* _Zak Seidov_, Jan 26 2009 *)

%o (PARI) a(n) = prod(k=1, n, prime(k))/2; \\ _Michel Marcus_, Mar 25 2017

%o (Python)

%o from sympy import primorial

%o def A070826(n): return primorial(n)>>1 # _Chai Wah Wu_, Jul 21 2022

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

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

%Y Range of A196529.

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, May 10 2002

%E Formula corrected by _Gary Detlefs_, Dec 07 2011