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

1,2

Comments

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A318456 A209085 A086799 * A308340 A161427 A365212

Adjacent sequences: A218385 A218386 A218387 * A218389 A218390 A218391

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Oct 27 2012

Status

approved