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A116883 A number k is included iff (highest odd divisor of k)^2 >= k.

%I A116883 #27 Oct 06 2024 13:10:06
%S A116883 1,3,5,6,7,9,10,11,13,14,15,17,18,19,20,21,22,23,25,26,27,28,29,30,31,
%T A116883 33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,58,
%U A116883 59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83
%N A116883 A number k is included iff (highest odd divisor of k)^2 >= k.
%C A116883 Also k is included if (and only if) the highest power of 2 dividing k is <= the largest odd divisor of k.
%e A116883 20 = 4 * 5, where 4 is highest power of 2 dividing 20 and 5 is the largest odd number dividing 20. 4 is <= 5 (and, not coincidentally, 5^2 >= 20), so 20 is in the sequence.
%p A116883 isA116883 := proc(n) local dvs,hod,i ; dvs := convert(numtheory[divisors](n),list) ; for i from 1 to nops(dvs) do hod := op(-i,dvs) ; if hod mod 2 = 1 then RETURN(hod^2 >= n) ; fi ; od ; end: for n from 1 to 200 do if isA116883(n) then printf("%d, ",n) ; fi ; od ; # _R. J. Mathar_, May 10 2007
%t A116883 Select[Range[100],Last[Select[Divisors[#],OddQ]]^2>=#&] (* _Harvey P. Dale_, Nov 10 2013 *)
%t A116883 Select[Range[100], # >= 4^IntegerExponent[#, 2] &] (* _Amiram Eldar_, Jun 11 2022 *)
%o A116883 (Python)
%o A116883 from itertools import count, islice
%o A116883 def A116883_gen(startvalue=1): # generator of terms >= startvalue
%o A116883     return filter(lambda n:n==1 or (n&-n)**2<n,count(max(startvalue,1)))
%o A116883 A116883_list = list(islice(A116883_gen(),30)) # _Chai Wah Wu_, Oct 06 2024
%Y A116883 Cf. A116882, A000265, A006519.
%K A116883 easy,nonn
%O A116883 1,2
%A A116883 _Leroy Quet_, Feb 24 2006
%E A116883 More terms from _R. J. Mathar_, May 10 2007