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A056195 a(n) = n! divided by its characteristic cube divisor A056194. 2
1, 2, 6, 3, 15, 720, 5040, 5040, 45360, 3628800, 39916800, 17740800, 230630400, 403603200, 1307674368, 20922789888, 355687428096, 51218989645824, 973160803270656, 2432902008176640000, 5516784599040000 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 21 10:28 EDT 2021. Contains 343149 sequences. (Running on oeis4.)