A089792 a(n) = n-(exponent of highest power of 3 dividing n!).

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, 15, 16, 16, 17, 18, 18, 19, 20, 19, 20, 21, 21, 22, 23, 23, 24, 25, 24, 25, 26, 26, 27, 28, 28, 29, 30, 28, 29, 30, 30, 31, 32, 32, 33, 34, 33

Offset: 0

Author

Paul Boddington, Jan 09 2004

Keywords

• easy
• nonn

Comments

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

Crossrefs

Cf. A007949, A054861, A125824.

Programs

Mathematica

Table[n-IntegerExponent[n!,3],{n,0,70}] (* Harvey P. Dale, Aug 09 2015 *)

PARI

vector(70, n, n--; n-valuation(n!, 3)) \\ Michel Marcus, Aug 19 2015

Formula

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

a(n) = log(denominator(n!/3^n))/log(3); a(n) = log_3(A125824(n)). - Paul Barry, Apr 02 2007

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