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
Amiram Eldar, Table of n, a(n) for n = 1..10000
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
KEYWORD
nonn,base
AUTHOR
Jason Earls, May 16 2004
STATUS
approved