A071637 Largest exponent k >=0 such that (n+1)^k divides n!.

0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 4, 0, 1, 2, 2, 0, 3, 0, 3, 2, 1, 0, 6, 2, 1, 3, 3, 0, 6, 0, 5, 2, 1, 4, 7, 0, 1, 2, 8, 0, 5, 0, 3, 9, 1, 0, 10, 3, 5, 2, 3, 0, 7, 4, 8, 2, 1, 0, 13, 0, 1, 9, 9, 4, 5, 0, 3, 2, 10, 0, 16, 0, 1, 8, 3, 6, 5, 0, 18, 9, 1, 0, 12, 4, 1, 2, 7, 0, 20, 6, 3, 2, 1, 4, 17, 0, 7, 8, 11

Offset

1,11

Comments

a(A068499(n)) = 0.

Links

Table of n, a(n) for n=1..99.

Example

12^4 divides 11! (11!/12^4=1925) but 12^5 doesn't, hence a(11)=4.

Mathematica

Table[IntegerExponent[n!, n+1], {n, 500}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

Prog

(PARI) for(n=1, 150, s=0; while(n!%(n+1)^s==0, s++); print1(s-1, ", "))

Crossrefs

A011776(n+1) - 1.

Sequence in context: A283675 A294653 A126222 * A141277 A198637 A365094

Adjacent sequences: A071634 A071635 A071636 * A071638 A071639 A071640

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 25 2002

Status

approved