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

1, 3, 30, 1680, 201600, 87091200, 1103619686400, 275463473725440000, 240529195987579699200000, 1163776461866305616609280000000, 344605941225348705438623229542400000000, 3717059729911125118574880410324812431360000000000

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..42

Mathematica

z=20;
nonprime = Join[{1}, Select[Range[250], CompositeQ]]; (* A018252 *)
f[j_]:= nonprime[[j]];
v[n_]:= Product[Product[f[k] - f[j], {j, 1, k-1}], {k, 2, n}];
d[n_]:= Product[(i-1)!, {i, 1, n}];
Table[v[n], {n, 1, z}]             (* this sequence *)
Table[v[n+1]/v[n], {n, 1, z}]      (* A203416 *)
Table[v[n]/d[n], {n, 1, z}]        (* A203417 *)

Prog

(Magma)
A018252:=[n : n in [1..250] | not IsPrime(n) ];
A203415:= func< n | n eq 1 select 1 else (&*[(&*[A018252[k+2] - A018252[j+1]: j in [0..k]]): k in [0..n-2]]) >;
[A203415(n): n in [1..30]]; // G. C. Greubel, Feb 29 2024
(SageMath)
A018252=[n for n in (1..250) if not is_prime(n)]
def A203415(n): return product(product(A018252[k+1]-A018252[j] for j in range(k+1)) for k in range(n-1))
[A203415(n) for n in range(1, 31)] # G. C. Greubel, Feb 29 2024

Crossrefs

Cf. A000040, A018252, A203416, A203417.

Sequence in context: A012008 A335710 A341499 * A203520 A238767 A323819

Adjacent sequences: A203412 A203413 A203414 * A203416 A203417 A203418

Keyword

nonn

Author

Clark Kimberling, Jan 01 2012

Status

approved