cp's OEIS Frontend

A203527 a(n) = Product_{1 <= i < j <= n} (A018252(i) + A018252(j)); A018252 = nonprime numbers.

%I A203527 #13 Jul 23 2017 13:19:06
%S A203527 1,5,350,529200,17542980000,14783258730240000,
%T A203527 511420331138811494400000,871980665589501641034301440000000,
%U A203527 60150685659205753788492548338089984000000000,182771197941564481989784945231570147139911680000000000000
%N A203527 a(n) = Product_{1 <= i < j <= n} (A018252(i) + A018252(j)); A018252 = nonprime numbers.
%C A203527 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 A203527 b:= proc(n) option remember; local k; if n=1 then 1
%p A203527       else for k from 1+b(n-1) while isprime(k) do od; k fi
%p A203527     end:
%p A203527 a:= n-> mul(mul(b(i)+b(j), i=1..j-1), j=2..n):
%p A203527 seq(a(n), n=1..10);  # _Alois P. Heinz_, Jul 23 2017
%t A203527 t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
%t A203527 nonprime = Rest[Union[t]]              (* A018252 *)
%t A203527 f[j_] := nonprime[[j]]; z = 20;
%t A203527 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203527 d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
%t A203527 Table[v[n], {n, 1, z}]                 (* A203527 *)
%t A203527 Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
%t A203527 Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)
%Y A203527 Cf. A018252, A203415, A203528, A203529.
%K A203527 nonn
%O A203527 1,2
%A A203527 _Clark Kimberling_, Jan 03 2012
%E A203527 Name edited by _Alois P. Heinz_, Jul 23 2017