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

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, 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, 9, 11, 8, 7, 8, 14, 8, 3, 13, 3, 5, 8, 7, 4, 10, 3, 10, 8

Offset: 1

Author

Reinhard Zumkeller, Jul 26 2011

Keywords

• nonn
• base
• look

Comments

a(n) >= A000005(n), a(A193460(n)) = A000005(A193460(n)).

Examples

			a(20) = #{1,2,4,5,10,20} = 6;
a(21) = #{1,2,3,4,6,7,12,21} = 8;
a(22) = #{1,2,11,22} = 4;
a(23) = #{1,2,4,8,16,23,32} = 7;
a(24) = #{1,2,3,4,6,7,8,12,14,21,24,42} = 12;
a(25) = #{1,2,4,5,13,25,26,52} = 8;
a(26) = #{1,2,13,26,31,62} = 6;
a(27) = #{1,2,3,4,6,8,9,12,18,24,27,36,72} = 13;
a(28) = #{1,2,4,7,14,28,41,82} = 8;
a(29) = #{1,2,4,23,29,46,92} = 7.
		

Links

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

Crossrefs

Cf. A047726.

Programs

Haskell

import Data.List (permutations, nub)
a193459 n =
   length $ nub $ concatMap divisors $ map read $ permutations $ show n
      where divisors n = filter ((== 0) . mod n) [1..n]
a193459_list = map a193459 [1..]