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 A203530 a(n) = Product_{1 <= i < j <= n} (c(i) + c(j)); c = A002808 = composite numbers. 4
 1, 10, 1680, 5569200, 426645273600, 1135354270482432000, 129053267560513803386880000, 556394398742051964595520667648000000, 99449133623220179596974346585642106880000000000 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 13 14:01 EDT 2022. Contains 356091 sequences. (Running on oeis4.)