A203418 Vandermonde determinant of the first n composite numbers (A002808).

1, 2, 16, 240, 11520, 13271040, 254803968000, 15892123484160000, 5126163351050649600000, 89288743527804466888704000000, 50689719717698351557731837542400000000, 125765178831579421305165126665125232640000000000

Offset: 1

Author

Clark Kimberling, Jan 02 2012

Keywords

• nonn

Comments

Each term divides its successor, as in A203419, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203420.

Links

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

Crossrefs

Cf. A000040, A000178, A002808, A203419, A203420.

Programs

Magma

A002808:=[n: n in [2..250] | not IsPrime(n)];
a:= func< n | n eq 0 select 1 else (&*[(&*[A002808[k+2] - A002808[j+1]: j in [0..k]]): k in [0..n-1]]) >;
[a(n): n in [0..20]]; // G. C. Greubel, Feb 24 2024

Mathematica

composite = Select[Range[100], CompositeQ]; (* A002808 *)
z = 20;
f[j_]:= composite[[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,z}]             (* this sequence *)
Table[v[n+1]/v[n], {n,z}]      (* A203419 *)
Table[v[n]/d[n], {n,z}]        (* A203420 *)

SageMath

A002808=[n for n in (2..250) if not is_prime(n)]
def a(n): return product(product( A002808[k+1] - A002808[j] for j in range(k+1)) for k in range(n))
[a(n) for n in range(15)] # G. C. Greubel, Feb 24 2024