A125824 -id:A125824 - cp's OEIS frontend

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

Paul Boddington, Jan 09 2004

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

Cf. A007949, A054861, A125824.

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

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

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).

A212307 Numerator of n!/3^n.

Original entry on oeis.org

1, 1, 2, 2, 8, 40, 80, 560, 4480, 4480, 44800, 492800, 1971200, 25625600, 358758400, 1793792000, 28700672000, 487911424000, 975822848000, 18540634112000, 370812682240000, 2595688775680000, 57105153064960000, 1313418520494080000, 10507348163952640000

Offset: 0

Jean-François Alcover and Paul Curtz, Oct 30 2013

Also the 3rd column of A152656 (or of A216919).

Cf. A001316, A049606, A125824 (denominators), A152656, A216919.

Cf. A000142, A060828.

Table[Numerator[n!/3^n], {n, 0, 32}]
(* or *) CoefficientList[Series[Exp[3x], {x, 0, 32}], x] // Denominator

a(n) = numerator(n!/3^n); \\ Michel Marcus, Oct 30 2013

a(n) = Product_{i=1..n} A038502(i). - Tom Edgar, Mar 22 2014

a(n) = A000142(n)/A060828(n). - Ridouane Oudra, Sep 23 2024

cp's OEIS Frontend

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

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