%I #11 Apr 21 2022 13:27:12

%S 0,1,2,2,3,4,4,5,6,5,6,7,7,8,9,9,10,11,10,11,12,12,13,14,14,15,16,14,

%T 15,16,16,17,18,18,19,20,19,20,21,21,22,23,23,24,25,24,25,26,26,27,28,

%U 28,29,30,28,29,30,30,31,32,32,33,34,33

%N a(n) = n-(exponent of highest power of 3 dividing n!).

%C The exponent of the highest power of 3 dividing binomial(n,k) is given by a(k)+a(n-k)-a(n).

%F a(n) = a(n-1)+1-A007949(n).

%F a(n) = log(denominator(n!/3^n))/log(3); a(n) = log_3(A125824(n)). - _Paul Barry_, Apr 02 2007

%F a(n) = n - A054861(n).

%t Table[n-IntegerExponent[n!,3],{n,0,70}] (* _Harvey P. Dale_, Aug 09 2015 *)

%o (PARI) vector(70, n, n--; n-valuation(n!, 3)) \\ _Michel Marcus_, Aug 19 2015

%Y Cf. A007949, A054861, A125824.

%K easy,nonn

%O 0,3

%A _Paul Boddington_, Jan 09 2004