A068741 -id:A068741 - cp's OEIS frontend

A068740 Result after dividing (n^n)! as many times as possible by n!.

1, 1, 3, 833712928048000000

Offset: 0

Henry Bottomley, Feb 26 2002

nonn

For prime n, it is also the number of generalized knockout tournament seedings with n players in one match and n rounds (see formula below). - Alexander Karpov, Dec 14 2017
Next term is too large to include.
From Robert G. Wilson v, Dec 14 2017: (Start)
a(4) = 4125147631...      (370 digits)...3291015625,
a(5) = 3483655217...     (7923 digits)...3819109376,
a(6) = 2196422024...   (164237 digits)...0161431552,
a(7) = 4948281440...  (4005981 digits)...0000000000,
a(8) = 4242413765...(102886160 digits)...4619140625,
(End)

			a(3)=833712928048000000 since 3!=6 and (3^3)!=27!=10888869450418352160768000000 which is divisible by 6^13=13060694016 but not 6^14=78364164096.

Robert G. Wilson v, Table of n, a(n) for n = 0..4
Alexander Karpov, Generalized knockout tournaments, National Research University Higher School of Economics. WP7/2017/03.

Cf. A000142, A000312, A023037, A057599, A068741, A068742.

a(n) = A068741(n)/A068742(n).

For p prime, a(p) = (p^p)!/(p!)^((p^p-1)/(p-1)).

A068742 Largest power of n! which divides (n^n)!.

Original entry on oeis.org

1, 1, 8, 13060694016, 2079483819621516594237312893208982470178235671604741236585936787960152492743230443701290222268785125031295963705114624

Offset: 0

Henry Bottomley, Feb 26 2002

nonn

			a(3)=13060694016 since (3^3)!=27!=10888869450418352160768000000 can be divided by 3!=6 thirteen times and 6^13=13060694016.

Cf. A000142, A000312, A023037, A068740, A068741.

for(n=2,10,p=1:f=(n^n)!:while(f%p==0,p=p*n!):print1(p/n!","))

For p prime, a(p)=(p!)^((p^p-1)/(p-1))

More terms from Ralf Stephan, Mar 31 2003

cp's OEIS Frontend

A068740 Result after dividing (n^n)! as many times as possible by n!.

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