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 A116882 A number n is included if (highest odd divisor of n)^2 <= n. 34
 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 If we define a divisor d|n to be superior if d >= n/d, then superior divisors are counted by A038548 and listed by A161908. This sequence consists of 1 and all numbers without a superior odd divisor. - Gus Wiseman, Feb 18 2021 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. Amelia Carolina Sparavigna, Discussion of the groupoid of Proth numbers (OEIS A080075), Politecnico di Torino, Italy (2019). 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. A000265, A006519, A080075, A112714. The complement is A116883. Positions of zeros (and 1) in A341675. A051283 = numbers without a superior prime-power divisor (zeros of A341593). A059172 = numbers without a superior squarefree divisor (zeros of A341592). A063539 = numbers without a superior prime divisor (zeros of A341591). A333805 counts strictly inferior odd divisors. A341594 counts strictly superior odd divisors. - Inferior: A033676, A038548, A063962, A066839, A069288, A161906, A217581. - Superior: A033677, A063538, A070038, A072500, A161908, A341676. - Strictly Inferior: A056924, A060775, A070039, A333806, A341596, A341674. - Strictly Superior: A056924, A064052/A048098, A140271, A238535, A341642, A341643, A341673. Cf. A000005, A000203, A001248, A006530, A020639, A026804, A027193, A340101, A340854 (zeros of A340832). Sequence in context: A326677 A330684 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 30 21:21 EDT 2022. Contains 357106 sequences. (Running on oeis4.)