A056195 a(n) = n! divided by its characteristic cube divisor A056194.

1, 2, 6, 3, 15, 720, 5040, 5040, 45360, 3628800, 39916800, 17740800, 230630400, 403603200, 1307674368, 20922789888, 355687428096, 51218989645824, 973160803270656, 2432902008176640000, 5516784599040000

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..491

Formula

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).

Example

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A337643 A071301 A145642 * A083169 A276817 A050125

Adjacent sequences: A056192 A056193 A056194 * A056196 A056197 A056198

Keyword

nonn

Author

Labos Elemer, Aug 02 2000

Status

approved