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A203533 a(n) = A203530(n)/A000178(n-1); A000178 = (superfactorials).

%I A203533 #13 Jan 13 2025 15:06:19
%S A203533 1,10,840,464100,1481407200,32851686067200,5186361382800998400,
%T A203533 4436556151786001058816000,19667253420867342693731328000000,
%U A203533 605862171333980479840975997239296000000,132207384898194165523202154782408753283072000000
%N A203533 a(n) = A203530(n)/A000178(n-1); A000178 = (superfactorials).
%C A203533 It is conjectured that every term is an integer.
%t A203533 t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
%t A203533 composite = Rest[Rest[Union[t]]]       (* A002808 *)
%t A203533 f[j_] := composite[[j]]; z = 20;
%t A203533 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203533 d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
%t A203533 Table[v[n], {n, 1, z}]                 (* A203530 *)
%t A203533 Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)
%t A203533 Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)
%Y A203533 Cf. A000178, A203530, A203532, A002808, A093883, A203420.
%K A203533 nonn
%O A203533 1,2
%A A203533 _Clark Kimberling_, Jan 03 2012