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

%I A203529 #13 Jan 13 2025 15:05:31
%S A203529 1,5,175,44100,60913125,427756329000,20552836095792000,
%T A203529 6952965728817588480000,11895516181976215338950400000,
%U A203529 99606443887767729350960121600000000,5830034964946921746536425070101217280000000
%N A203529 a(n) = A203527(n)/A000178(n-1); A000178 = (superfactorials).
%C A203529 It is conjectured that every term is an integer.
%t A203529 t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
%t A203529 nonprime = Rest[Union[t]]              (* A018252 *)
%t A203529 f[j_] := nonprime[[j]]; z = 20;
%t A203529 v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
%t A203529 d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)
%t A203529 Table[v[n], {n, 1, z}]                 (* A203527 *)
%t A203529 Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203528 *)
%t A203529 Table[v[n]/d[n], {n, 1, 20}]           (* A203529 *)
%Y A203529 Cf. A000178, A203527, A203528, A018252, A093883, A203417.
%K A203529 nonn
%O A203529 1,2
%A A203529 _Clark Kimberling_, Jan 03 2012