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

1,6

Comments

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

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.

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

Example

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

Mathematica

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

Prog

(Sage)
n=200 #change n for more terms
[6^(valuation(i, 6)) for i in [1..n]]
(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
(PARI) a(n)=6^valuation(n, 6) \\ Charles R Greathouse IV, Aug 05 2015

Crossrefs

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

Sequence in context: A267426 A202917 A324396 * A325471 A167155 A369465

Adjacent sequences: A234956 A234957 A234958 * A234960 A234961 A234962

Keyword

nonn,easy

Author

Tom Edgar, Jan 01 2014

Status

approved