A203418
Vandermonde determinant of the first n composite numbers (A002808).
Original entry on oeis.org
1, 2, 16, 240, 11520, 13271040, 254803968000, 15892123484160000, 5126163351050649600000, 89288743527804466888704000000, 50689719717698351557731837542400000000, 125765178831579421305165126665125232640000000000
Offset: 1
-
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
-
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 *)
-
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
Original entry on oeis.org
1, 2, 8, 20, 40, 384, 10240, 126720, 1013760, 48660480, 7612661760, 473174507520, 16701626253312, 4036421002199040, 407426244909465600, 23814785343474892800, 932976775107465707520, 26694111965427724713984, 9044593230639040844267520
Offset: 1
-
A002808:=[n: n in [2..250] | not IsPrime(n)];
BarnesG:= func< n | (&*[Factorial(k): k in [0..n-2]]) >;
a:= func< n | n eq 1 select 1 else (&*[(&*[A002808[k+2] - A002808[j+1]: j in [0..k]]): k in [0..n-2]])/BarnesG(n+1) >;
[a(n): n in [1..40]]; // G. C. Greubel, Feb 24 2024
-
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}] (* A203418 *)
Table[v[n+1]/v[n], {n,z}] (* A203419 *)
Table[v[n]/d[n], {n,z}] (* this sequence *)
-
A002808=[n for n in (2..250) if not is_prime(n)]
def BarnesG(n): return product(factorial(j) for j in range(1,n-1))
def a(n): return product(product(A002808[k+1] - A002808[j] for j in range(k+1)) for k in range(n-1))/BarnesG(n+1)
[a(n) for n in range(1,41)] # G. C. Greubel, Feb 24 2024
Original entry on oeis.org
10, 168, 3315, 76608, 2661120, 113667840, 4311354600, 178738560000, 11178747740160, 791853627801600, 44783640216315000, 2693449157020876800, 246209683227475968000, 17126298576096297588000, 1253392853589570355200000
Offset: 1
-
t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
composite = Rest[Rest[Union[t]]] (* A002808 *)
f[j_] := composite[[j]]; z = 20;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
Table[v[n], {n, 1, z}] (* A203530 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203532 *)
Table[v[n]/d[n], {n, 1, 20}] (* A203533 *)
Showing 1-3 of 3 results.
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