A203419 - OEIS

%I #12 Feb 24 2024 11:03:45

%S 2,8,15,48,1152,19200,62370,322560,17418240,567705600,2481078600,

%T 16907304960,1504935936000,8799558768000,76435881984000,

%U 819678899239200,10176845001523200,2169274855587840000,215013524533936128000

%N a(n) = A203418(n+1)/A203418(n).

%H G. C. Greubel, <a href="/A203419/b203419.txt">Table of n, a(n) for n = 1..350</a>

%t composite = Select[Range[100], CompositeQ]; (* A002808 *)

%t z = 20;

%t f[j_]:= composite[[j]];

%t v[n_]:= Product[Product[f[k] - f[j], {j, 1, k - 1}], {k, 2, n}];

%t d[n_]:= Product[(i-1)!, {i, 1, n}];

%t Table[v[n], {n,z}]           (* A203418 *)

%t Table[v[n+1]/v[n], {n,z}]    (* this sequence *)

%t Table[v[n]/d[n], {n,z}]      (* A203420 *)

%o (Magma)

%o A002808:=[n: n in [2..250] | not IsPrime(n)];

%o a:= func< n | (&*[A002808[n+1] - A002808[j+1]: j in [0..n-1]]) >;

%o [a(n): n in [1..40]]; // _G. C. Greubel_, Feb 24 2024

%o (SageMath)

%o A002808=[n for n in (2..250) if not is_prime(n)]

%o def a(n): return product(A002808[n] - A002808[j] for j in range(n))

%o [a(n) for n in range(1,41)] # _G. C. Greubel_, Feb 24 2024

%Y Cf. A000040, A002808, A003418, A203418, A203420.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 02 2012