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A239826 Sum of divisors of n that are also suffixes of n in binary representation. 2

%I #9 Aug 06 2014 02:24:18

%S 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,

%T 28,31,32,30,38,32,32,34,36,36,40,38,40,43,48,42,44,44,48,51,48,48,64,

%U 50,52,55,56,54,62,56,64,58,60,60,76,62,64,74,64,66,68,68

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

%H Reinhard Zumkeller, <a href="/A239826/b239826.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e . n | divisors | . . . in binary | a(n)

%e . ---+----------------+---------------------------+--------------------

%e . 10 | 1,2,5,10 | 1,10,101,1010 | 2 + 10 | 12

%e . 11 | 1,11 | 1,1011 | 1 + 11 | 12

%e . 12 | 1,2,3,4,6,12 | 1,10,11,100,110,1100 | 4 + 12 | 16

%e . 13 | 1,13 | 1,1101 | 1 + 13 | 14

%e . 14 | 1,2,7,14 | 1,10,111,1110 | 2 + 14 | 16

%e . 15 | 1,3,5,15 | 1,11,101,1111 | 1 + 3 + 15 | 19

%e . 16 | 1,2,4,8,16 | 1,10,100,1000,10000 | 16 | 16

%e . 17 | 1,17 | 1,10001 | 1 + 17 | 18

%e . 18 | 1,2,3,6,9,18 | 1,10,11,110,1001,10010 | 2 + 18 | 20

%e . 19 | 1,19 | 1,10011 | 1 + 19 | 20

%e . 20 | 1,2,4,5,10,20 | 1,10,100,101,1010,10100 | 4 + 20 | 24;

%e a(63) = 1 + 3 + 7 + 63 = 74;

%e a(735) = 1 + 3 + 7 + 15 + 735 = 761;

%e a(4095) = 1 + 3 + 7 + 15 + 63 + 4095 = 4185;

%e a(185535) = 1 + 3 + 7 + 15 + 31 + 63 + 185535 = 185655.

%o (Haskell)

%o import Data.List (isPrefixOf); import Data.Function (on)

%o a239826 n = sum $

%o filter ((flip isPrefixOf `on` a030308_row) n) $ a027750_row n

%o -- _Reinhard Zumkeller_, Mar 27 2014

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 27 2014

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)