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A203415 Vandermonde determinant of the first n nonprimes (A018252). 5

%I

%S 1,3,30,1680,201600,87091200,1103619686400,275463473725440000,

%T 240529195987579699200000,1163776461866305616609280000000,

%U 344605941225348705438623229542400000000,3717059729911125118574880410324812431360000000000

%N Vandermonde determinant of the first n nonprimes (A018252).

%C Each term divides its successor, as in A203416, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203417.

%t t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];

%t nonprime = Rest[Union[t]];

%t f[j_] := nonprime[[j]]; z = 20; (* A018252 *)

%t v[n_] := Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}]

%t d[n_] := Product[(i - 1)!, {i, 1, n}]

%t Table[v[n], {n, 1, z}] (* A203415 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203416 *)

%t Table[v[n]/d[n], {n, 1, 20}] (* A203417 *)

%Y Cf. A203416, A203417, A000040, A018252.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 01 2012

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Last modified August 11 03:07 EDT 2020. Contains 336421 sequences. (Running on oeis4.)