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A093696
Numbers n such that all divisors of n have an odd number of 1's in their binary expansions.
11
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
OFFSET
1,2
COMMENTS
Subsequence of A000069. - Michel Marcus, Feb 09 2014
Numbers all of whose divisors are odious. - Bernard Schott, Jul 22 2022
LINKS
FORMULA
{n: A356018(n) =0 }. - R. J. Mathar, Aug 07 2022
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
(Python)
from sympy import divisors, isprime
def c(n): return bin(n).count("1")&1
def ok(n): return n > 0 and all(c(d) for d in divisors(n, generator=True))
print([k for k in range(174) if ok(k)]) # Michael S. Branicky, Jul 24 2022
CROSSREFS
Similar sequences: A062687, A190217, A337741, A337941, A355596.
A000079 is a subsequence.
Sequence in context: A089559 A165741 A238989 * A190851 A325427 A336656
KEYWORD
nonn,base
AUTHOR
Jason Earls, May 16 2004
STATUS
approved