A203415
Vandermonde determinant of the first n nonprimes (A018252).
Original entry on oeis.org
1, 3, 30, 1680, 201600, 87091200, 1103619686400, 275463473725440000, 240529195987579699200000, 1163776461866305616609280000000, 344605941225348705438623229542400000000, 3717059729911125118574880410324812431360000000000
Offset: 1
-
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
-
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 *)
-
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
Original entry on oeis.org
1, 3, 15, 140, 700, 2520, 44352, 2196480, 47567520, 634233600, 51753461760, 13984935444480, 1448751906201600, 82605199597240320, 32797812715211980800, 5296846753506734899200, 483765735240908144640000, 28985693293514522492928000
Offset: 1
-
A018252:=[n : n in [1..250] | not IsPrime(n) ];
BarnesG:= func< n | (&*[Factorial(k): k in [0..n-2]]) >;
v:= func< n | n eq 1 select 1 else (&*[(&*[A018252[k+2] - A018252[j+1]: j in [0..k]]): k in [0..n-2]]) >;
[v(n)/BarnesG(n+1): n in [1..30]]; // G. C. Greubel, Feb 29 2024
-
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}] (* A203415 *)
Table[v[n + 1]/v[n], {n,1,z}] (* A203416 *)
Table[v[n]/d[n], {n,1,z}] (* this sequence *)
-
A018252=[n for n in (1..250) if not is_prime(n)]
def BarnesG(n): return product(factorial(j) for j in range(1, n-1))
def v(n): return product(product(A018252[k-1]-A018252[j-1] for j in range(1,k)) for k in range(2,n+1))
[v(n)/BarnesG(n+1) for n in range(1,31)] # G. C. Greubel, Feb 29 2024
A203528
a(n) = v(n+1)/v(n), where v=A203527.
Original entry on oeis.org
5, 70, 1512, 33150, 842688, 34594560, 1705017600, 68981673600, 3038555520000, 212396207063040, 16628926183833600, 985240084758930000, 61949330611480166400, 6155242080686899200000, 445283762978503737288000
Offset: 1
-
t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];
nonprime = Rest[Union[t]] (* A018252 *)
f[j_] := nonprime[[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}] (* A203527 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203528 *)
Table[v[n]/d[n], {n, 1, 20}] (* A203529 *)
Showing 1-3 of 3 results.
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