A203530 - OEIS

%I #16 Jul 23 2017 13:44:53

%S 1,10,1680,5569200,426645273600,1135354270482432000,

%T 129053267560513803386880000,556394398742051964595520667648000000,

%U 99449133623220179596974346585642106880000000000

%N a(n) = Product_{1 <= i < j <= n} (c(i) + c(j)); c = A002808 = composite numbers.

%C Each term divides its successor, as in A203530.

%C It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n); as in A203533.

%C See A093883 for a guide to related sequences.

%p c:= proc(n) option remember; local k; if n=1 then 4

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

%p     end:

%p a:= n-> mul(mul(c(i)+c(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 composite = Rest[Rest[Union[t]]]       (* A002808 *)

%t f[j_] := composite[[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}]                 (* A203530 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)

%t Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)

%Y Cf. A002808, A203418, A203532, A203533.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 03 2012

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