A203524 a(n) = Product_{2 <= i < j <= n+1} (prime(i) + prime(j)).

1, 8, 960, 3870720, 535088332800, 4746447547269120000, 2251903055463146166681600000, 101133031075657891684280256430080000000, 764075218501479062478490016486870993810227200000000, 510692344365454233151092604262379676645631378616169267200000000000

Offset: 1

Author

Clark Kimberling, Jan 03 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203525. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n); as in A203526. See A093883 for a guide to related sequences.

Crossrefs

Cf. A000040, A203315, A203525, A203526.

Programs

Maple

a:= n-> mul(mul(ithprime(i)+ithprime(j), i=2..j-1), j=3..n+1):
seq(a(n), n=1..10);  # Alois P. Heinz, Jul 23 2017

Mathematica

f[j_] := Prime[j + 1]; z = 17;
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}]                   (* A203524 *)
Table[v[n + 1]/(8 v[n]), {n, 1, z - 1}]  (* A203525 *)
Table[v[n]/d[n], {n, 1, 20}]             (* A203526 *)

Extensions

Name edited by Alois P. Heinz, Jul 23 2017