A056195 - OEIS

%I #12 Sep 06 2020 03:46:12

%S 1,2,6,3,15,720,5040,5040,45360,3628800,39916800,17740800,230630400,

%T 403603200,1307674368,20922789888,355687428096,51218989645824,

%U 973160803270656,2432902008176640000,5516784599040000

%N a(n) = n! divided by its characteristic cube divisor A056194.

%H Amiram Eldar, <a href="/A056195/b056195.txt">Table of n, a(n) for n = 1..491</a>

%F The CCD of n! is the cube of g = A055229(n!) = A055230(n). So a(n) = n!/ggg = L*L*f where L = A000188(n!)/A055229(n!) = A055772(n)/A055230(n) and f = A055231(n!) = A055773(n).

%e n = 10, a(10) = 10! because g(10!) = 1.

%e n = 9, a(9) = 45320 because 9! = 2*2*2*2*2*2*2*3*3*5*7 and g(9!) = 2, so a(9) = 9!/8.

%t f[p_, e_] := If[OddQ[e] && e > 1, p^3, 1]; a[n_] := n! / (Times @@ f @@@ FactorInteger[n!]); Array[a, 20] (* _Amiram Eldar_, Sep 06 2020 *)

%Y Cf. A055229, A055230, A055071, A055772, A055773.

%K nonn

%O 1,2

%A _Labos Elemer_, Aug 02 2000