A203530 a(n) = Product_{1 <= i < j <= n} (c(i) + c(j)); c = A002808 = composite numbers.

1, 10, 1680, 5569200, 426645273600, 1135354270482432000, 129053267560513803386880000, 556394398742051964595520667648000000, 99449133623220179596974346585642106880000000000

Offset: 1

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203530.

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

See A093883 for a guide to related sequences.

Crossrefs

Cf. A002808, A203418, A203532, A203533.

Programs

Maple

c:= proc(n) option remember; local k; if n=1 then 4
      else for k from 1+c(n-1) while isprime(k) do od; k fi
    end:
a:= n-> mul(mul(c(i)+c(j), i=1..j-1), j=2..n):
seq(a(n), n=1..10);  # Alois P. Heinz, Jul 23 2017

Mathematica

t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
composite = Rest[Rest[Union[t]]]       (* A002808 *)
f[j_] := composite[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
Table[v[n], {n, 1, z}]                 (* A203530 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)

Extensions

Name edited by Alois P. Heinz, Jul 23 2017