%I #13 Jul 23 2017 13:19:06

%S 1,5,350,529200,17542980000,14783258730240000,

%T 511420331138811494400000,871980665589501641034301440000000,

%U 60150685659205753788492548338089984000000000,182771197941564481989784945231570147139911680000000000000

%N a(n) = Product_{1 <= i < j <= n} (A018252(i) + A018252(j)); A018252 = nonprime numbers.

%C Each term divides its successor, as in A203528. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n); as in A203529. See A093883 for a guide to related sequences.

%p b:= proc(n) option remember; local k; if n=1 then 1

%p else for k from 1+b(n-1) while isprime(k) do od; k fi

%p end:

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

%p seq(a(n), n=1..10); # _Alois P. Heinz_, Jul 23 2017

%t t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];

%t nonprime = Rest[Union[t]] (* A018252 *)

%t f[j_] := nonprime[[j]]; z = 20;

%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}] (* A203527 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203528 *)

%t Table[v[n]/d[n], {n, 1, 20}] (* A203529 *)

%Y Cf. A018252, A203415, A203528, A203529.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 03 2012

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