A218403 Bitwise OR of all proper divisors of n; a(1) = 0 by convention.

0, 1, 1, 3, 1, 3, 1, 7, 3, 7, 1, 7, 1, 7, 7, 15, 1, 15, 1, 15, 7, 11, 1, 15, 5, 15, 11, 15, 1, 15, 1, 31, 11, 19, 7, 31, 1, 19, 15, 31, 1, 31, 1, 31, 15, 23, 1, 31, 7, 31, 19, 31, 1, 31, 15, 31, 19, 31, 1, 31, 1, 31, 31, 63, 13, 63, 1, 55, 23, 47, 1, 63, 1

Offset: 1

Author

Reinhard Zumkeller, Oct 28 2012

Keywords

• nonn
• base
• look

Examples

			n=20: properDivisors(20) = {1, 2, 4, 5, 10}, 0001 OR 0010 OR 0100 OR 0101 OR 1010 = 1111 -> a(20) = 15;
n=21: properDivisors(21) = {1, 3, 7}, 001 OR 011 OR 111 = 111 -> a(21) = 7;
n=22: properDivisors(22) = {1, 2, 11}, 0001 OR 0010 OR 1011 = 1111 -> a(22) = 11;
n=23: properDivisors(23) = {1} -> a(23) = 23;
n=24: properDivisors(24) = {1, 2, 3, 4, 6, 8, 12}, 0001 OR 0010 OR 0011 OR 0100 OR 0110 OR 1000 OR 1100 = 1111 -> a(24) = 15;
n=25: properDivisors(25) = {1, 5}, 001 OR 101 = 101 -> a(25) = 5.
		

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. A001065, A027751, A000225 (subsequence), A123345, A227320, A293214, A293215.

Programs

Haskell

import Data.Bits ((.|.))
a218403 = foldl (.|.)  0 . a027751_row :: Integer -> Integer

Mathematica

Table[BitOr@@Most[Divisors[n]],{n,80}] (* Harvey P. Dale, Nov 09 2012 *)

PARI

A218403(n) = { my(s=0); fordiv(n,d,if(dAntti Karttunen, Oct 08 2017

Formula

a(n) <= A218388(n).

a(A000040(n)) = 1.

From Antti Karttunen, Oct 08 2017: (Start)

a(n) = A087207(A293214(n)).

A227320(n) <= a(n) <= A001065(n).

(End)