A080941 Greatest proper divisor of n which is a suffix of n in binary representation; a(n) = 0 if no such divisor exists.

0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 4, 1, 2, 3, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 6, 1, 0, 1, 2, 1, 4, 1, 2, 3, 8, 1, 2, 1, 4, 5, 2, 1, 16, 1, 2, 3, 4, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 7, 0, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 4, 1, 6, 1, 16, 1, 2, 1, 4, 5, 2, 3, 8, 1, 10, 1, 4, 1, 2, 1, 32, 1, 2, 3, 4, 1, 6, 1

Offset

1,6

Comments

a(n)=0 iff n=2^k (A000079);

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

n=30='11110', divisors<30: 1='1', 2='10', 3='11', 5='101', 6='110', 10='1010' and 15='1111', therefore a(30)=2='10';
n=31='11111', divisors<31: 1='1', therefore a(31)=1;
n=32='100000', divisors<32: 1='1', 2='10', 4='100', 8='1000' and 16='10000', therefore a(32)=0.

Prog

(Haskell)
import Data.List (isPrefixOf); import Data.Function (on)
a080941 n = if null ds then 0 else head ds  where
            ds = filter ((flip isPrefixOf `on` a030308_row) n) $
                        reverse $ a027751_row n
-- Reinhard Zumkeller, Mar 27 2014

Crossrefs

Cf. A007088, A080940, A080942.

Cf. A030308, A027751.

Sequence in context: A345221 A346633 A080940 * A346705 A177405 A379110

Adjacent sequences: A080938 A080939 A080940 * A080942 A080943 A080944

Keyword

nonn,base

Author

Reinhard Zumkeller, Feb 25 2003

Extensions

Definition improved by Reinhard Zumkeller, Mar 27 2014

Status

approved