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

1, 1, 8, 13060694016, 2079483819621516594237312893208982470178235671604741236585936787960152492743230443701290222268785125031295963705114624

Offset

0,3

Links

Table of n, a(n) for n=0..4.

Formula

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

Example

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

Prog

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

Crossrefs

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

Sequence in context: A004740 A108067 A067486 * A272826 A019440 A085276

Adjacent sequences: A068739 A068740 A068741 * A068743 A068744 A068745

Keyword

nonn

Author

Henry Bottomley, Feb 26 2002

Extensions

More terms from Ralf Stephan, Mar 31 2003

Status

approved