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

1,2

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.

Links

Table of n, a(n) for n=1..9.

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 *)

Crossrefs

Cf. A002808, A203418, A203532, A203533.

Sequence in context: A204466 A117523 A203696 * A232594 A194793 A211915

Adjacent sequences: A203527 A203528 A203529 * A203531 A203532 A203533

Keyword

nonn

Author

Clark Kimberling, Jan 03 2012

Extensions

Name edited by Alois P. Heinz, Jul 23 2017

Status

approved