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A359708 a(n) is the greatest divisor d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.

%I A359708 #13 Jan 14 2023 08:46:22
%S A359708 1,2,1,4,5,3,1,8,9,10,1,6,1,2,1,16,17,18,1,20,21,2,1,12,5,2,9,7,1,3,1,
%T A359708 32,33,34,1,36,37,19,1,40,41,42,1,4,5,2,1,24,1,25,17,4,1,18,1,14,1,2,
%U A359708 1,6,1,2,1,64,65,66,1,68,69,35,1,72,73,74,1,38,1
%N A359708 a(n) is the greatest divisor d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.
%C A359708 Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.
%H A359708 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F A359708 a(n) = n iff n belongs to A003714.
%e A359708 For n = 12:
%e A359708 - we have (with AND denoting the bitwise AND operator):
%e A359708     d   d AND 24
%e A359708     --  --------
%e A359708      1         0
%e A359708      2         0
%e A359708      3         0
%e A359708      4         0
%e A359708      6         0
%e A359708      8         8
%e A359708     12         8
%e A359708     24        24
%e A359708 - hence a(12) = 6.
%o A359708 (PARI) a(n) = fordiv (n, d, if (bitand(n/d, 2*n)==0, return (n/d)))
%Y A359708 Cf. A003714, A359627.
%K A359708 nonn,base
%O A359708 1,2
%A A359708 _Rémy Sigrist_, Jan 12 2023