A075068 -id:A075068 - cp's OEIS frontend

A262206 Product of prime(n) consecutive numbers starting from n.

2, 24, 2520, 604800, 54486432000, 53353114214400, 35905578804006912000, 80018147048929689600000, 203939450748460387344384000000, 1441310123089178548721360295690240000000, 9218619547278385997621820451234775040000000

Offset: 1

Altug Alkan, Sep 15 2015

a(n) is always divisible by A039716(n).

			For n=1, a(1) = 1*2 = 2.
For n=2, a(2) = 2*3*4 = 24.
For n=3, a(3) = 3*4*5*6*7 = 2520.
For n=4, a(4) = 4*5*6*7*8*9*10 = 604800.

Cf. A075069: product of prime(n) consecutive numbers starting from prime(n).

Cf. A014688, A039716, A075068, A262204.

[Factorial(NthPrime(n)+n-1)/Factorial(n-1): n in [1..15]]; // Vincenzo Librandi, Sep 16 2015

A262206:=n->(ithprime(n)+n-1)! / (n-1)!: seq(A262206(n), n=1..15); # Wesley Ivan Hurt, Sep 15 2015

Table[(Prime[n] + n - 1)!/(n - 1)!, {n, 15}] (* Michael De Vlieger, Sep 15 2015 *)

a(n) = (prime(n)+n-1)! / (n-1)!;
vector(15,n,a(n))

a(n)=factorback([n..n+prime(n)-1]) \\ Charles R Greathouse IV, Sep 21 2015

a(n) = (prime(n) + n - 1)! / (n-1)!.

A110342 a(1) = 1; a(n) = product of n successive primes beginning with n if n is prime else product of n successive composite numbers beginning with n.

Original entry on oeis.org

1, 6, 105, 1728, 85085, 725760, 215656441, 522547200, 27433728000, 1609445376000, 2928046583754721, 2824576634880000, 50774191064678342417, 6327051662131200000, 507067997493657600000, 42593711789467238400000

Offset: 1

Amarnath Murthy, Jul 20 2005

nonn

Contains A075068 as a subsequence. - R. J. Mathar, Mar 05 2008

nextNonprime := proc(n) local a; for a from n+1 do if not isprime(a) then RETURN(a) ; fi ; od: end: A110342 := proc(n) local res,cnt,nfac; res := n ; if isprime(n) then nfac := nextprime(n) ; for cnt from 2 to n do res := res*nfac ; nfac := nextprime(nfac) ; od: else nfac := nextNonprime(n) ; for cnt from 2 to n do res := res*nfac ; nfac := nextNonprime(nfac) ; od: fi; RETURN(res) ; end: seq(A110342(n),n=1..30) ; # R. J. Mathar, Mar 05 2008

More terms from R. J. Mathar, Mar 05 2008

cp's OEIS Frontend

A262206 Product of prime(n) consecutive numbers starting from n.

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