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

1,2

Links

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

Index entries for sequences related to binary expansion of n

Example

.   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.

Prog

(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

Crossrefs

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

Sequence in context: A132118 A221952 A007843 * A246601 A288529 A288772

Adjacent sequences: A239823 A239824 A239825 * A239827 A239828 A239829

Keyword

nonn

Author

Reinhard Zumkeller, Mar 27 2014

Status

approved