A203528 -id:A203528 - cp's OEIS frontend

A203527 a(n) = Product_{1 <= i < j <= n} (A018252(i) + A018252(j)); A018252 = nonprime numbers.

1, 5, 350, 529200, 17542980000, 14783258730240000, 511420331138811494400000, 871980665589501641034301440000000, 60150685659205753788492548338089984000000000, 182771197941564481989784945231570147139911680000000000000

Offset: 1

Clark Kimberling, Jan 03 2012

nonn

Each term divides its successor, as in A203528. It is conjectured that each term is divisible by the corresponding superfactorial, A000178(n); as in A203529. See A093883 for a guide to related sequences.

Cf. A018252, A203415, A203528, A203529.

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

t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
nonprime = Rest[Union[t]]              (* A018252 *)
f[j_] := nonprime[[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}]                 (* A203527 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)

Name edited by Alois P. Heinz, Jul 23 2017

A203529 a(n) = A203527(n)/A000178(n-1); A000178 = (superfactorials).

Original entry on oeis.org

1, 5, 175, 44100, 60913125, 427756329000, 20552836095792000, 6952965728817588480000, 11895516181976215338950400000, 99606443887767729350960121600000000, 5830034964946921746536425070101217280000000

Offset: 1

Clark Kimberling, Jan 03 2012

nonn

It is conjectured that every term is an integer.

Cf. A000178, A203527, A203528, A018252, A093883, A203417.

t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
nonprime = Rest[Union[t]]              (* A018252 *)
f[j_] := nonprime[[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}]                 (* A203527 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)

cp's OEIS Frontend

A203527 a(n) = Product_{1 <= i < j <= n} (A018252(i) + A018252(j)); A018252 = nonprime numbers.

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