A218388 Bitwise OR of all divisors of n.

1, 3, 3, 7, 5, 7, 7, 15, 11, 15, 11, 15, 13, 15, 15, 31, 17, 31, 19, 31, 23, 31, 23, 31, 29, 31, 27, 31, 29, 31, 31, 63, 43, 51, 39, 63, 37, 55, 47, 63, 41, 63, 43, 63, 47, 63, 47, 63, 55, 63, 51, 63, 53, 63, 63, 63, 59, 63, 59, 63, 61, 63, 63, 127, 77, 127

Offset: 1

Author

Reinhard Zumkeller, Oct 27 2012

Keywords

• nonn
• base
• look

Comments

a(n) <= A003817(n); a(A000040(n)) = A000040(n).

Examples

			n=20: divisors(20) = {1, 2, 4, 5, 10, 20}, 00001 OR 00010 OR 00100 OR 00101 OR 01010 OR 10100 = 11111 -> a(20) = 31;
n=21: divisors(21) = {1, 3, 7, 21}, 00001 OR 00011 OR 00111 OR 10101 = 10111 -> a(21) = 23;
n=22: divisors(22) = {1, 2, 11, 22}, 00001 OR 00010 OR 01011 OR 10110 = 11111 -> a(22) = 31;
n=23: divisors(23) = {1, 23}, 00001 OR 10111 = 10111 -> a(23) = 23;
n=24: divisors(24) = {1, 2, 3, 4, 6, 8, 12, 24}, 00001 OR 00010 OR 00011 OR 00100 OR 00110 OR 01000 OR 01100 OR 11000 = 11111 -> a(24) = 31;
n=25: divisors(25) = {1, 5, 25}, 00001 OR 00101 OR 11001 = 11101 -> a(25) = 29.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..8191
• Eric Weisstein's World of Mathematics, OR
• Wikipedia, Bitwise operation OR
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A027750, A000225 (subsequence), A123345, A218403.

Programs

Haskell

import Data.Bits ((.|.))
a218388 = foldl1 (.|.) . a027750_row :: Integer -> Integer

Mathematica

Table[BitOr@@Divisors[n],{n,70}] (* Harvey P. Dale, Feb 27 2013 *)