A239826 Sum of divisors of n that are also suffixes of n in binary representation.

1, 2, 4, 4, 6, 8, 8, 8, 10, 12, 12, 16, 14, 16, 19, 16, 18, 20, 20, 24, 22, 24, 24, 32, 26, 28, 31, 32, 30, 38, 32, 32, 34, 36, 36, 40, 38, 40, 43, 48, 42, 44, 44, 48, 51, 48, 48, 64, 50, 52, 55, 56, 54, 62, 56, 64, 58, 60, 60, 76, 62, 64, 74, 64, 66, 68, 68

Offset: 1

Author

Reinhard Zumkeller, Mar 27 2014

Keywords

• nonn

Examples

			.   n | divisors       |  . . . in binary          |               a(n)
.  ---+----------------+---------------------------+--------------------
.  10 | 1,2,5,10       |  1,10,101,1010            |  2 + 10     |  12
.  11 | 1,11           |  1,1011                   |  1 + 11     |  12
.  12 | 1,2,3,4,6,12   |  1,10,11,100,110,1100     |  4 + 12     |  16
.  13 | 1,13           |  1,1101                   |  1 + 13     |  14
.  14 | 1,2,7,14       |  1,10,111,1110            |  2 + 14     |  16
.  15 | 1,3,5,15       |  1,11,101,1111            |  1 + 3 + 15 |  19
.  16 | 1,2,4,8,16     |  1,10,100,1000,10000      |  16         |  16
.  17 | 1,17           |  1,10001                  |  1 + 17     |  18
.  18 | 1,2,3,6,9,18   |  1,10,11,110,1001,10010   |  2 + 18     |  20
.  19 | 1,19           |  1,10011                  |  1 + 19     |  20
.  20 | 1,2,4,5,10,20  |  1,10,100,101,1010,10100  |  4 + 20     |  24;
a(63) = 1 + 3 + 7 + 63 = 74;
a(735) = 1 + 3 + 7 + 15 + 735 = 761;
a(4095) = 1 + 3 + 7 + 15 + 63 + 4095 = 4185;
a(185535) = 1 + 3 + 7 + 15 + 31 + 63 + 185535 = 185655.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A030308, A027750, A080942, A000203, A007088.

Programs

Haskell

import Data.List (isPrefixOf); import Data.Function (on)
a239826 n = sum $
            filter ((flip isPrefixOf `on` a030308_row) n) $ a027750_row n
-- Reinhard Zumkeller, Mar 27 2014