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A203521 a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).

%I A203521 #26 Jul 26 2017 14:29:41
%S A203521 1,1,5,280,302400,15850598400,32867800842240000,
%T A203521 5539460271229108224000000,55190934927547677562078494720000000,
%U A203521 61965661927377302817151474643396198400000000000,14512955968670787590604912803260278557019929051136000000000000
%N A203521 a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).
%C A203521 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 A203521 Alois P. Heinz, <a href="/A203521/b203521.txt">Table of n, a(n) for n = 0..32</a>
%e A203521 a(1) = 1.
%e A203521 a(2) = 2 + 3 = 5.
%e A203521 a(3) = (2+3)(2+5)(3+5) = 280.
%p A203521 a:= n-> mul(mul(ithprime(i)+ithprime(j), i=1..j-1), j=2..n):
%p A203521 seq(a(n), n=0..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203521 f[j_] := Prime[j]; z = 15;
%t A203521 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203521 d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
%t A203521 Table[v[n], {n, 1, z}]                (* A203521 *)
%t A203521 Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
%t A203521 Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)
%Y A203521 Cf. A000040, A080358, A203522, A203523, A203524.
%K A203521 nonn
%O A203521 0,3
%A A203521 _Clark Kimberling_, Jan 03 2012
%E A203521 Name edited by _Alois P. Heinz_, Jul 23 2017