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A116882 A number n is included if (highest odd divisor of n)^2 <= n. 4
1, 2, 4, 8, 12, 16, 24, 32, 40, 48, 56, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384, 416, 448, 480, 512, 544, 576, 608, 640, 672, 704, 736, 768, 800, 832, 864, 896, 928, 960, 992, 1024, 1088, 1152, 1216, 1280, 1344, 1408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also n is included if (and only if ) the greatest power of 2 dividing n is >= the highest odd divisor of n. All terms of the sequence are even besides the 1.

Equivalently, positive integers of the form k*2^m, where odd k <= 2^m. - Thomas Ordowski, Oct 19 2014

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.

FORMULA

a(n) = A080075(n-1)-1. - Klaus Brockhaus, Georgi Guninski and M. F. Hasler, Aug 16 2010

a(n) ~ n^2/2. - Thomas Ordowski, Oct 19 2014

EXAMPLE

40 = 8 * 5, where 8 is highest power of 2 dividing 40 and 5 is the highest odd dividing 40. 8 is >= 5 (and, uncoincidently, 5^2 <= 40), so 40 is in the sequence.

MATHEMATICA

f[n_] := Select[Divisors[n], OddQ[ # ] &][[ -1]]; Insert[Select[Range[2, 1500], 2^FactorInteger[ # ][[1]][[2]] > f[ # ] &], 1, 1] (* Stefan Steinerberger, Apr 10 2006 *)

PROG

(PARI) isok(n) = vecmax(select(x->((x % 2)==1), divisors(n)))^2 <= n; \\ Michel Marcus, Sep 06 2016

CROSSREFS

Cf. A116883, A000265, A006519.

Sequence in context: A246692 A181824 A070173 * A069519 A087980 A181818

Adjacent sequences:  A116879 A116880 A116881 * A116883 A116884 A116885

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 24 2006

EXTENSIONS

More terms from Stefan Steinerberger, Apr 10 2006

STATUS

approved

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Last modified June 25 06:13 EDT 2017. Contains 288709 sequences.