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A227921 Odd odious numbers (A000069), all divisors of which are odious. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)