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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[ # ][][] > 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 (PARI) isok(n) = 2^(valuation(n, 2)*2) >= n \\ Jeppe Stig Nielsen, Feb 19 2019 CROSSREFS Cf. A116883, A000265, A006519, A080075, A112714. 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 September 23 05:06 EDT 2019. Contains 327327 sequences. (Running on oeis4.)