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A193459 Total number of distinct divisors of all numbers that can be written by rearranging the digits of n in decimal representation.

%I A193459 #11 Jan 29 2014 04:05:25
%S A193459 1,2,2,3,2,4,2,4,3,4,2,8,3,5,6,6,3,8,5,6,8,4,7,12,8,6,13,8,7,8,3,7,4,
%T A193459 5,5,12,3,5,6,8,5,12,5,6,11,9,5,16,6,6,6,8,5,11,4,11,8,7,5,12,6,6,12,
%U A193459 9,11,8,7,8,14,8,3,13,3,5,8,7,4,10,3,10,8
%N A193459 Total number of distinct divisors of all numbers that can be written by rearranging the digits of n in decimal representation.
%C A193459 a(n) >= A000005(n), a(A193460(n)) = A000005(A193460(n)).
%H A193459 Reinhard Zumkeller, <a href="/A193459/b193459.txt">Table of n, a(n) for n = 1..10000</a>
%e A193459 a(20) = #{1,2,4,5,10,20} = 6;
%e A193459 a(21) = #{1,2,3,4,6,7,12,21} = 8;
%e A193459 a(22) = #{1,2,11,22} = 4;
%e A193459 a(23) = #{1,2,4,8,16,23,32} = 7;
%e A193459 a(24) = #{1,2,3,4,6,7,8,12,14,21,24,42} = 12;
%e A193459 a(25) = #{1,2,4,5,13,25,26,52} = 8;
%e A193459 a(26) = #{1,2,13,26,31,62} = 6;
%e A193459 a(27) = #{1,2,3,4,6,8,9,12,18,24,27,36,72} = 13;
%e A193459 a(28) = #{1,2,4,7,14,28,41,82} = 8;
%e A193459 a(29) = #{1,2,4,23,29,46,92} = 7.
%o A193459 (Haskell)
%o A193459 import Data.List (permutations, nub)
%o A193459 a193459 n =
%o A193459    length $ nub $ concatMap divisors $ map read $ permutations $ show n
%o A193459       where divisors n = filter ((== 0) . mod n) [1..n]
%o A193459 a193459_list = map a193459 [1..]
%Y A193459 Cf. A047726.
%K A193459 nonn,base,look
%O A193459 1,2
%A A193459 _Reinhard Zumkeller_, Jul 26 2011