A047726 - OEIS

A047726

Number of different numbers that are formed by permuting digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 6

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OFFSET

1,10

COMMENTS

The minimum value of a(A171102(n)) is 10*9!. - Altug Alkan, Jul 08 2016

LINKS

A. Dunigan AtLee, Table of n, a(n) for n = 1..100000.

FORMULA

a(n) << n / (log_10 n)^4.5 by Stirling's approximation. - Charles R Greathouse IV, Sep 29 2011

a(n) = A000142(A055642(n))/Product_{k=0..9} A000142(A100910(n,k)). - Robert Israel, Jul 08 2016

EXAMPLE

From 102 we get 102, 120, 210, 201, 12 and 21, so a(102)=6.

From 33950 with 5 digits, one '0', two '3', one '5' and one '9', we get 5! / (1! * 2! * 1! * 1!) = 60 different numbers and a(33950) = 60. - Bernard Schott, Oct 20 2019

MAPLE

f:= proc(n) local L;

L:= convert(n, base, 10);

nops(L)!/mul(numboccur(i, L)!, i=0..9);

end proc:

map(f, [$1..1000]); # Robert Israel, Jul 08 2016

MATHEMATICA

pd[n_]:=Module[{p=Permutations[IntegerDigits[n]]}, Length[Union [FromDigits/@p]]]; pd/@Range[120] (* Harvey P. Dale, Mar 22 2011 *)

PROG

(Haskell)

import Data.List (permutations, nub)

a047726 n = length $ nub $ permutations $ show n