

A075309


Distinctdigit perfect powers.


6



1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 125, 128, 169, 196, 216, 243, 256, 289, 324, 361, 512, 529, 576, 625, 729, 784, 841, 961, 1024, 1089, 1296, 1369, 1728, 1764, 1849, 1936, 2048, 2187, 2197, 2304, 2401, 2601, 2704, 2809, 2916, 3025, 3125, 3249, 3481
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Of 1110 perfect powers < 1000000, 259 are distinctdigit.
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
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


LINKS

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


EXAMPLE

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


MAPLE

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


MATHEMATICA

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 *)


CROSSREFS

Cf. A001597, A090516.
Sequence in context: A076292 A090516 A090515 * A175031 A052054 A046447
Adjacent sequences: A075306 A075307 A075308 * A075310 A075311 A075312


KEYWORD

easy,nonn,base,fini,full


AUTHOR

Zak Seidov, Oct 11 2002


EXTENSIONS

More terms from David Wasserman, Jan 16 2005


STATUS

approved



