1,2

Of 1110 perfect powers < 1000000, 259 are distinct-digit.

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

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

T. D. Noe, Table of n, a(n) for n=1..657

100,121,144,343 etc. are not members.

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)

Cf. A090516, A001597.

Adjacent sequences: A075306 A075307 A075308 this_sequence A075310 A075311 A075312

Sequence in context: A076292 A090516 A090515 this_sequence A052054 A046447 A087244

easy,nonn,base,fini

Zak Seidov (zakseidov(AT)yahoo.com), Oct 11 2002

More terms from David Wasserman (dwasserm(AT)earthlink.net), Jan 16 2005