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Highest power of 9 dividing n!.
4

%I #5 Jun 07 2016 16:48:12

%S 0,0,0,0,0,0,1,1,1,2,2,2,2,2,2,3,3,3,4,4,4,4,4,4,5,5,5,6,6,6,7,7,7,7,

%T 7,7,8,8,8,9,9,9,9,9,9,10,10,10,11,11,11,11,11,11,13,13,13,13,13,13,

%U 14,14,14,15,15,15,15,15,15,16,16,16,17,17,17,17,17,17,18,18,18,20,20,20,20

%N Highest power of 9 dividing n!.

%F a(n) =A090622(n, 9) =[A054861(n)/2] =[([n/3]+[n/9]+[n/27]+[n/81]+...)/2].

%e a(9)=2 since 9!=362880=9^2*4480.

%t IntegerExponent[Range[0,90]!,9] (* _Harvey P. Dale_, Jun 07 2016 *)

%Y Cf. A011371, A054861, A090616, A027868, A054896, A090617.

%K nonn

%O 0,10

%A _Henry Bottomley_, Dec 06 2003