A128993 - OEIS

%I #9 May 09 2018 10:47:21

%S 125,512,144,441,169,196,961,243,324,256,625,1024,2401,1089,9801,1296,

%T 2916,9216,1369,1936,1728,2187,1764,4761,2197,7921,4096,9604,10201,

%U 12100,10404,14400,40401,44100,10609,16900,19600,61009,90601,96100

%N A table which contains in each row two or more perfect powers with the same digits.

%C Perfect powers, A001597, may have anagrams (obtained by permutation of the digits, excluding anagrams with leading zeros) which are again perfect powers. Each row of the table collects a set of at least two different anagrams which are perfect powers.

%C Requiring at least two different representations in a row means that numbers like 81 = 3^4 = 9^2, which are in A117453, do not necessarily populate a row on their own.

%C The table is sorted such that entries in the first column are increasing, and such that each perfect power appears at most once.

%e The table starts with the first 11 rows as follows:

%e 125,512; 125=5^3 and 512 = 2^9 = 8^3

%e 144,441; 144=12^2 and 441=21^2

%e 169,196,961; 169=13^2 and 196=14^2 and 961=31^2

%e 243,324; 243=3^5 and 324=18^2

%e 256,625; 256 = 16^2=4^4 and 625=25^2=5^4

%e 1024,2401; 1024=2^10=32^2 and 2401=49^2=7^4

%e 1089,9801; 1089=33^2 and 9801=99^2

%e 1296,2916,9216; 1296=36^2 and 2916=54^2 and 9216=96^2

%e 1369,1936; 1369=37^2 and 1936=44^2

%e 1728,2187; 1728=12^3 and 2187=3^7

%e 1764,4761; 1764=42^2 and 4761=69^2

%Y Cf. A117453.

%K nonn,base,tabf

%O 1,1

%A _J. M. Bergot_, Apr 30 2007

%E Edited, and most terms replaced by _R. J. Mathar_, Nov 02 2009