A203521 - OEIS

%I #26 Jul 26 2017 14:29:41

%S 1,1,5,280,302400,15850598400,32867800842240000,

%T 5539460271229108224000000,55190934927547677562078494720000000,

%U 61965661927377302817151474643396198400000000000,14512955968670787590604912803260278557019929051136000000000000

%N a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).

%C 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.

%H Alois P. Heinz, <a href="/A203521/b203521.txt">Table of n, a(n) for n = 0..32</a>

%e a(1) = 1.

%e a(2) = 2 + 3 = 5.

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

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

%p seq(a(n), n=0..10);  # _Alois P. Heinz_, Jul 23 2017

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

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

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

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

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

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

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

%K nonn

%O 0,3

%A _Clark Kimberling_, Jan 03 2012

%E Name edited by _Alois P. Heinz_, Jul 23 2017