%I #22 Aug 14 2017 02:42:59
%S 1,4,8,9,16,25,27,32,36,49,64,81,125,128,169,196,216,243,256,289,324,
%T 361,512,529,576,625,729,784,841,961,1024,1089,1296,1369,1728,1764,
%U 1849,1936,2048,2187,2197,2304,2401,2601,2704,2809,2916,3025,3125,3249,3481
%N Distinct-digit perfect powers.
%C Of 1110 perfect powers < 1000000, 259 are distinct-digit.
%C Sequence is finite. What is the index of the last term? Note that 2^30 = 1073741824, hence the highest power that occurs < 30. The frequency chart of a power r, 2 < r < 30 may be of some interest and could be included. - _Amarnath Murthy_, Dec 06 2003
%C There are a total of 657 distinct terms, the last of which is 99066^2=9814072356. The highest power occurs in 2^29. There are 609 squares, 39 cubes, 19 fourth powers, 9 fifth powers, 4 sixth powers, 4 seventh powers, 3 eighth powers, 2 ninth powers, 2 tenth powers and one each of powers 11, 12, 13, 14, 15, 20 and 29. These counts to not add to 657 because 1 is not counted and some powers, such as 2^4 = 4^2 = 16, are counted twice. - _T. D. Noe_, Aug 09 2005
%H T. D. Noe, <a href="/A075309/b075309.txt">Table of n, a(n) for n = 1..657</a> (full sequence)
%e 100,121,144,343 etc. are not members.
%p lim:=floor(sqrt(9876543210)): A075309:={1}: for n from 2 to lim do k:=2: p:=n^k: while p<=9876543210 do p:=n^k: pandig:=true: d:=convert(p, base, 10): for j from 0 to 9 do if(numboccur(j, d)>1)then pandig:=false: break: fi: od: if(pandig)then A075309 := A075309 union {p}: fi: k:=k+1: od: od: op(sort(convert(A075309, list))); # _Nathaniel Johnston_, Jun 23 2011
%t lst={1}; Do[k=1; While[k++; n=k^pow; n<10^10, d=IntegerDigits[n]; If[Length[Union[d]]==Length[d], AppendTo[lst, n]]], {pow, 2, 29}]; lst=Union[lst] (* _T. D. Noe_ *)
%Y Cf. A001597, A090516.
%K easy,nonn,base,fini,full
%O 1,2
%A _Zak Seidov_, Oct 11 2002
%E More terms from _David Wasserman_, Jan 16 2005