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
3, 10, 56, 120, 432, 12672, 249600, 873180, 4838400, 296110080, 10786406400, 49621572000, 355053404160, 34613526528000, 211189410432000, 1910897049600000, 21311651380219200, 274774815041126400, 62908970812047360000
Offset: 1
-
A018252:=[n : n in [1..250] | not IsPrime(n) ];
A203416:= func< n | n eq 1 select 3 else (&*[A018252[n+1] - A018252[j+1]: j in [0..n-1]]) >;
[A203416(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}] (* A203415 *)
Table[v[n+1]/v[n], {n,1,z}] (* this sequence *)
Table[v[n]/d[n], {n,1,z}] (* A203417 *)
-
A018252=[n for n in (1..250) if not is_prime(n)]
def A203416(n): return product(A018252[n]-A018252[j] for j in range(n))
[A203416(n) for n in range(1,31)] # G. C. Greubel, Feb 29 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
1, 5, 175, 44100, 60913125, 427756329000, 20552836095792000, 6952965728817588480000, 11895516181976215338950400000, 99606443887767729350960121600000000, 5830034964946921746536425070101217280000000
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 1-4 of 4 results.
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