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A268355 Highest power of 8 dividing n. 1
1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

The generalized binomial coefficients produced by this sequence provide an analog to Kummer's Theorem using arithmetic in base 8.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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.

Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

FORMULA

a(n) = 8^valuation(n,8).

a(n) = 8^A244413(n).

G.f.: Sum_{m>=0} 8^m * Sum_{j=1..7} x^(j*8^m)/(1-x^(8^(m+1))). - Robert Israel, Feb 03 2016

EXAMPLE

Since 16 = 8 * 2, a(16) = 8. Likewise, since 8 does not divide 15, a(15) = 1.

MAPLE

seq(8^floor(padic:-ordp(n, 2)/3), n=1..100); # Robert Israel, Feb 03 2016

MATHEMATICA

8^Table[IntegerExponent[n, 8], {n, 150}] (* Vincenzo Librandi, Feb 03 2016 *)

PROG

(Sage) [8^valuation(i, 8) for i in [1..100]]

(PARI) a(n) = 8^valuation(n, 8); \\ Michel Marcus, Feb 05 2016

CROSSREFS

Cf. A006519, A038500, A234957, A244413, A234959.

Sequence in context: A199461 A056191 A103760 * A008834 A056201 A088842

Adjacent sequences:  A268352 A268353 A268354 * A268356 A268357 A268358

KEYWORD

nonn,easy,mult

AUTHOR

Tom Edgar, Feb 02 2016

EXTENSIONS

Keyword:mult added by Andrew Howroyd, Jul 20 2018

STATUS

approved

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Last modified January 18 13:55 EST 2020. Contains 331010 sequences. (Running on oeis4.)