A203523 -id:A203523 - cp's OEIS frontend

A203521 a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).

1, 1, 5, 280, 302400, 15850598400, 32867800842240000, 5539460271229108224000000, 55190934927547677562078494720000000, 61965661927377302817151474643396198400000000000, 14512955968670787590604912803260278557019929051136000000000000

Offset: 0

Clark Kimberling, Jan 03 2012

nonn

Each term divides its successor, as in A203511. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n). See A093883 for a guide to related sequences.

			a(1) = 1.
a(2) = 2 + 3 = 5.
a(3) = (2+3)(2+5)(3+5) = 280.

Alois P. Heinz, Table of n, a(n) for n = 0..32

Cf. A000040, A080358, A203522, A203523, A203524.

a:= n-> mul(mul(ithprime(i)+ithprime(j), i=1..j-1), j=2..n):
seq(a(n), n=0..10);  # Alois P. Heinz, Jul 23 2017

f[j_] := Prime[j]; z = 15;
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}]                (* A203521 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)

Name edited by Alois P. Heinz, Jul 23 2017

A203522 a(n) = v(n+1)/v(n), where v = A203521.

Original entry on oeis.org

1, 5, 56, 1080, 52416, 2073600, 168537600, 9963233280, 1122750720000, 234209649623040, 22056529195008000, 5634088861040640000, 1027073825689514803200, 132063784535221862400000, 27917533370401003929600000

Offset: 0

Clark Kimberling, Jan 03 2012

nonn

Robert Israel, Table of n, a(n) for n = 0..290
Robert Israel, Table of n, a(n) for n = 1..290

Cf. A203522, A203523, A000040, A093883.

f:= proc(n) local i; mul(ithprime(i)+ithprime(n+1),i=1..n) end proc:
map(f, [$1..30]); # Robert Israel, Jan 28 2025

f[j_] := Prime[j]; z = 15;
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}]                (* A203521 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]   (* A203522 *)
Table[v[n]/d[n], {n, 1, 20}]          (* A203523 *)

a(n) = Product_{i=1..n} (prime(i)+prime(n+1)). - Robert Israel, Jan 28 2025

a(0) = 1 inserted by Robert Israel, Jan 29 2025

cp's OEIS Frontend

A203521 a(n) = Product_{1 <= i < j <= n} (prime(i) + prime(j)).

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