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

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, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83

Offset: 1

Author

Leroy Quet, Feb 24 2006

Keywords

• easy
• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A116882, A000265, A006519.

Programs

Maple

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

Mathematica

Select[Range[100],Last[Select[Divisors[#],OddQ]]^2>=#&] (* Harvey P. Dale, Nov 10 2013 *)
Select[Range[100], # >= 4^IntegerExponent[#, 2] &] (* Amiram Eldar, Jun 11 2022 *)

Python

from itertools import count, islice
def A116883_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:n==1 or (n&-n)**2A116883_list = list(islice(A116883_gen(),30)) # Chai Wah Wu, Oct 06 2024

Extensions

More terms from R. J. Mathar, May 10 2007