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A203521 a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)). 6
1, 1, 5, 280, 302400, 15850598400, 32867800842240000, 5539460271229108224000000, 55190934927547677562078494720000000, 61965661927377302817151474643396198400000000000, 14512955968670787590604912803260278557019929051136000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Each term divides its successor, as in A203511. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n). See A093883 for a guide to related sequences.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..32

EXAMPLE

a(1) = 1.

a(2) = 2 + 3 = 5.

a(3) = (2+3)(2+5)(3+5) = 280.

MAPLE

a:= n-> mul(mul(ithprime(i)+ithprime(j), i=1..j-1), j=2..n):

seq(a(n), n=0..10);  # Alois P. Heinz, Jul 23 2017

MATHEMATICA

f[j_] := Prime[j]; z = 15;

v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)

Table[v[n], {n, 1, z}]                (* A203521 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)

Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)

CROSSREFS

Cf. A000040, A080358, A203522, A203523, A203524.

Sequence in context: A225781 A057209 A216662 * A276556 A283569 A252173

Adjacent sequences:  A203518 A203519 A203520 * A203522 A203523 A203524

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 03 2012

EXTENSIONS

Name edited by Alois P. Heinz, Jul 23 2017

STATUS

approved

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Last modified December 15 16:15 EST 2018. Contains 318150 sequences. (Running on oeis4.)