cp's OEIS Frontend

A047726 Number of different numbers that are formed by permuting digits of n.

%I A047726 #50 Oct 21 2019 03:24:30
%S A047726 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,
%T A047726 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,
%U A047726 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
%N A047726 Number of different numbers that are formed by permuting digits of n.
%C A047726 The minimum value of a(A171102(n)) is 10*9!. - _Altug Alkan_, Jul 08 2016
%H A047726 A. Dunigan AtLee, <a href="/A047726/b047726.txt">Table of n, a(n) for n = 1..100000</a>.
%F A047726 a(n) << n / (log_10 n)^4.5 by Stirling's approximation. - _Charles R Greathouse IV_, Sep 29 2011
%F A047726 a(n) = A000142(A055642(n))/Product_{k=0..9} A000142(A100910(n,k)). - _Robert Israel_, Jul 08 2016
%e A047726 From 102 we get 102, 120, 210, 201, 12 and 21, so a(102)=6.
%e A047726 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
%p A047726 f:= proc(n) local L;
%p A047726   L:= convert(n,base,10);
%p A047726   nops(L)!/mul(numboccur(i,L)!,i=0..9);
%p A047726 end proc:
%p A047726 map(f, [$1..1000]); # _Robert Israel_, Jul 08 2016
%t A047726 pd[n_]:=Module[{p=Permutations[IntegerDigits[n]]},Length[Union [FromDigits/@p]]]; pd/@Range[120]  (* _Harvey P. Dale_, Mar 22 2011 *)
%o A047726 (Haskell)
%o A047726 import Data.List (permutations, nub)
%o A047726 a047726 n = length $ nub $ permutations $ show n
%o A047726 -- _Reinhard Zumkeller_, Jul 26 2011
%o A047726 (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
%o A047726 (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
%Y A047726 Cf. A055098. Identical to A043537 and A043562 for n<100.
%Y A047726 Cf. A179239. - _Aaron Dunigan AtLee_, Jul 14 2010
%K A047726 nonn,easy,base,nice
%O A047726 1,10
%A A047726 _N. J. A. Sloane_
%E A047726 Corrected by _Henry Bottomley_, Apr 19 2000