A227921 Odd odious numbers (A000069), all divisors of which are odious.

1, 7, 11, 13, 19, 31, 37, 41, 47, 49, 59, 61, 67, 73, 79, 91, 97, 103, 107, 109, 121, 127, 131, 133, 137, 143, 151, 157, 167, 173, 179, 181, 191, 193, 199, 211, 217, 223, 227, 229, 233, 239, 241, 247, 251, 259, 271, 283, 307, 313, 331, 341, 361, 367, 379, 397, 403

Offset

1,2

Comments

All primes are in A027697.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

odious:= proc(n) option remember;
  n::odd xor procname(floor(n/2))
end proc:
odious(0):= false:
odious(1):= true:
filter:= proc(n) andmap(odious, numtheory:-divisors(n)) end proc:
select(filter, [seq(i, i=1..500, 2)]); # Robert Israel, Aug 18 2019

Mathematica

odiusQ[n_]:=OddQ[Total[IntegerDigits[n, 2]]]; Select[Range[1, 411, 2], odiusQ[ #]&&AllTrue[Divisors[#], odiusQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 08 2019 *)

Prog

(PARI) isodious(n) = {b = binary(n); sum(i=1, #b, b[i]==1) % 2; }
isok(n) = {if (!(n % 2), return (0)); fordiv(n, div, if (! isodious(div), return (0))); return (1); } \\ Michel Marcus, Oct 12 2013

Crossrefs

Cf. A000069, A027697.

Sequence in context: A245179 A297177 A239710 * A176620 A059637 A059308

Adjacent sequences: A227918 A227919 A227920 * A227922 A227923 A227924

Keyword

nonn,base

Author

Vladimir Shevelev, Oct 09 2013

Status

approved