A161399 a(n) = the smallest divisor of n that contains the same number of (non-leading) 0's as n when both numbers are written in binary.

1, 2, 1, 4, 5, 2, 1, 8, 9, 10, 11, 4, 13, 2, 1, 16, 17, 18, 19, 20, 21, 22, 23, 8, 25, 26, 27, 4, 29, 2, 1, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 9, 46, 47, 16, 49, 50, 51, 52, 53, 9, 5, 8, 19, 58, 59, 4, 61, 2, 1, 64, 65, 66, 67, 68, 69, 70, 71

Offset

1,2

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Maple

with(numtheory):
z:= proc(n) local m, r; m, r:=n, 0;
      while m>1 do r:= r+1-irem(m, 2, 'm'); r od
    end:
a:= proc(n) local d, t; t:=z(n);
      for d in sort([divisors(n)[]]) do
        if z(d)=t then return d fi od
    end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 23 2013

Mathematica

sdn[n_]:=SelectFirst[Divisors[n], DigitCount[#, 2, 0]==DigitCount[n, 2, 0]&]; Array[sdn, 80] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Sep 05 2015 *)

Crossrefs

Cf. A161398.

Sequence in context: A090077 A229763 A163509 * A318479 A053985 A091564

Adjacent sequences: A161396 A161397 A161398 * A161400 A161401 A161402

Keyword

base,nonn

Author

Leroy Quet, Jun 09 2009

Status

approved