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

1, 1, 8, 13060694016, 2079483819621516594237312893208982470178235671604741236585936787960152492743230443701290222268785125031295963705114624

Offset: 0

Author

Henry Bottomley, Feb 26 2002

Keywords

• nonn

Examples

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

Crossrefs

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

Programs

PARI

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

Formula

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

Extensions

More terms from Ralf Stephan, Mar 31 2003