A203530 - OEIS

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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

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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