%I A075309
%S A075309 1,4,8,9,16,25,27,32,36,49,64,81,125,128,169,196,216,243,256,289,324,
%T A075309 361,512,529,576,625,729,784,841,961,1024,1089,1296,1369,1728,1764,1849,
%U A075309 1936,2048,2187,2197,2304,2401,2601,2704,2809,2916,3025,3125,3249,3481
%N A075309 Distinct-digit perfect powers.
%C A075309 Of 1110 perfect powers < 1000000, 259 are distinct-digit.
%C A075309 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 (amarnath_murthy(AT)yahoo.com), Dec 
               06 2003
%C A075309 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 (noe(AT)sspectra.com), Aug 09 2005
%H A075309 T. D. Noe, <a href="b075309.txt">Table of n, a(n) for n=1..657</a>
%e A075309 100,121,144,343 etc. are not members.
%t A075309 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] (Noe)
%Y A075309 Cf. A090516, A001597.
%Y A075309 Sequence in context: A076292 A090516 A090515 this_sequence A175031 A052054 
               A046447
%Y A075309 Adjacent sequences: A075306 A075307 A075308 this_sequence A075310 A075311 
               A075312
%K A075309 easy,nonn,base,fini
%O A075309 1,2
%A A075309 Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002
%E A075309 More terms from David Wasserman (dwasserm(AT)earthlink.net), Jan 16 2005