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A093696 Numbers n such that all divisors of n have an odd number of 1's in their binary expansions. 6
1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 22, 26, 28, 31, 32, 37, 38, 41, 44, 47, 49, 52, 56, 59, 61, 62, 64, 67, 73, 74, 76, 79, 82, 88, 91, 94, 97, 98, 103, 104, 107, 109, 112, 118, 121, 122, 124, 127, 128, 131, 133, 134, 137, 143, 146, 148, 151, 152, 157, 158, 164, 167, 173 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Subsequence of A000069. - Michel Marcus, Feb 09 2014

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

14 is in the sequence because its divisors are [1, 2, 7, 14] and in binary: 1, 10, 111 and 1110, all have an odd number of 1's.

MAPLE

isA001969 := proc(n)

    if wt(n) mod 2 = 0 then

        true;

    else

        false;

    end if;

end proc:

isA093696 := proc(n)

    for d in numtheory[divisors](n) do

        if isA001969(d) then

            return false;

        end if;

    end do;

    true;

end proc:

for n from 1 to 200 do

    if isA093696(n) then

        printf("%d, ", n);

    end if;

end do: # R. J. Mathar, Feb 13 2014

MATHEMATICA

odiousQ[n_] := OddQ @ DigitCount[n, 2][[1]]; Select[Range[200], AllTrue[ Divisors[#], odiousQ ] &] (* Amiram Eldar, Dec 09 2019 *)

PROG

(PARI) is(n)=fordiv(n, d, if(hammingweight(d)%2==0, return(0))); 1 \\ Charles R Greathouse IV, Mar 29 2013

CROSSREFS

Cf. A001969, A093688.

Sequence in context: A089559 A165741 A238989 * A190851 A325427 A336656

Adjacent sequences:  A093693 A093694 A093695 * A093697 A093698 A093699

KEYWORD

nonn,base

AUTHOR

Jason Earls, May 16 2004

STATUS

approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)