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.

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, 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, 1, 6, 1, 2, 1, 64, 65, 66, 1, 68, 69, 35, 1, 72, 73, 74, 1, 38, 1

Offset: 1

Author

Rémy Sigrist, Jan 12 2023

Keywords

• nonn
• base

Comments

Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.

Examples

			For n = 12:
- we have (with AND denoting the bitwise AND operator):
    d   d AND 24
    --  --------
     1         0
     2         0
     3         0
     4         0
     6         0
     8         8
    12         8
    24        24
- hence a(12) = 6.
		

Links

• Index entries for sequences related to divisors

Crossrefs

Cf. A003714, A359627.

Programs

PARI

a(n) = fordiv (n, d, if (bitand(n/d, 2*n)==0, return (n/d)))

Formula

a(n) = n iff n belongs to A003714.