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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base
• nice

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A055098. Identical to A043537 and A043562 for n<100.

Cf. A179239. - Aaron Dunigan AtLee, Jul 14 2010

Programs

Haskell

import Data.List (permutations, nub)
a047726 n = length $ nub $ permutations $ show n
-- Reinhard Zumkeller, Jul 26 2011

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 *)

PARI

a(n)=n=eval(Vec(Str(n)));(#n)!/prod(i=0,9,sum(j=1,#n,n[j]==i)!) \\ Charles R Greathouse IV, Sep 29 2011

PARI

A047726(n)={local(c=Vec(0,10)); apply(d->c[d+1]++, digits(n)); logint(n*10,10)!/prod(i=1,10,c[i]!)} \\ M. F. Hasler, Oct 18 2019

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

Extensions

Corrected by Henry Bottomley, Apr 19 2000