A234959 Highest power of 6 dividing n.

1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 6

Offset: 1

Author

Tom Edgar, Jan 01 2014

Keywords

• nonn
• easy

Comments

The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 6.

Examples

			Since 12 = 6 * 2, a(12) = 6. Likewise, since 6 does not divide 13, a(13) = 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.

Crossrefs

Cf. A006519, A038500, A122841, A234957, A243758.

Programs

Haskell

a234959 = f 1 where
   f y x = if m == 0 then f (y * 6) x' else y  where (x', m) = divMod x 6
-- Reinhard Zumkeller, Feb 09 2015

Mathematica

6^Table[IntegerExponent[n, 6], {n, 84}] (* Alonso del Arte, Jan 01 2014 *)

PARI

a(n)=6^valuation(n,6) \\ Charles R Greathouse IV, Aug 05 2015

Sage

n=200 #change n for more terms
[6^(valuation(i,6)) for i in [1..n]]

Formula

a(n) = 6^(valuation(n,6)).

a(n) = 6^A122841(n). - Joerg Arndt, Jan 02 2014

G.f.: x/(1 - x) + 5 * Sum_{k>=1} 6^(k-1)*x^(6^k)/(1 - x^(6^k)). - Ilya Gutkovskiy, Jul 10 2019