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A number k is included iff (highest odd divisor of k)^2 >= k.
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%I #27 Oct 06 2024 13:10:06

%S 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 33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,58,

%U 59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83

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

%C Also k is included if (and only if) the highest power of 2 dividing k is <= the largest odd divisor of k.

%e 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 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 Select[Range[100],Last[Select[Divisors[#],OddQ]]^2>=#&] (* _Harvey P. Dale_, Nov 10 2013 *)

%t Select[Range[100], # >= 4^IntegerExponent[#, 2] &] (* _Amiram Eldar_, Jun 11 2022 *)

%o (Python)

%o from itertools import count, islice

%o def A116883_gen(startvalue=1): # generator of terms >= startvalue

%o return filter(lambda n:n==1 or (n&-n)**2<n,count(max(startvalue,1)))

%o A116883_list = list(islice(A116883_gen(),30)) # _Chai Wah Wu_, Oct 06 2024

%Y Cf. A116882, A000265, A006519.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Feb 24 2006

%E More terms from _R. J. Mathar_, May 10 2007