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
Examples
12^4 divides 11! (11!/12^4=1925) but 12^5 doesn't, hence a(11)=4.
Crossrefs
A011776(n+1) - 1.
Programs
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Mathematica
Table[IntegerExponent[n!,n+1],{n,500}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *) -
PARI
for(n=1,150,s=0; while(n!%(n+1)^s==0,s++); print1(s-1,","))
Comments