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

1,10

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
-- Reinhard Zumkeller, Jul 26 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

Crossrefs

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

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

Sequence in context: A297778 A043562 A043537 * A297779 A043563 A043538

Adjacent sequences: A047723 A047724 A047725 * A047727 A047728 A047729

Keyword

nonn,easy,base,nice

Author

N. J. A. Sloane

Extensions

Corrected by Henry Bottomley, Apr 19 2000

Status

approved