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A128993 A table which contains in each row two or more perfect powers with the same digits.

%I A128993 #9 May 09 2018 10:47:21
%S A128993 125,512,144,441,169,196,961,243,324,256,625,1024,2401,1089,9801,1296,
%T A128993 2916,9216,1369,1936,1728,2187,1764,4761,2197,7921,4096,9604,10201,
%U A128993 12100,10404,14400,40401,44100,10609,16900,19600,61009,90601,96100
%N A128993 A table which contains in each row two or more perfect powers with the same digits.
%C A128993 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 A128993 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 A128993 The table is sorted such that entries in the first column are increasing, and such that each perfect power appears at most once.
%e A128993 The table starts with the first 11 rows as follows:
%e A128993 125,512; 125=5^3 and 512 = 2^9 = 8^3
%e A128993 144,441; 144=12^2 and 441=21^2
%e A128993 169,196,961; 169=13^2 and 196=14^2 and 961=31^2
%e A128993 243,324; 243=3^5 and 324=18^2
%e A128993 256,625; 256 = 16^2=4^4 and 625=25^2=5^4
%e A128993 1024,2401; 1024=2^10=32^2 and 2401=49^2=7^4
%e A128993 1089,9801; 1089=33^2 and 9801=99^2
%e A128993 1296,2916,9216; 1296=36^2 and 2916=54^2 and 9216=96^2
%e A128993 1369,1936; 1369=37^2 and 1936=44^2
%e A128993 1728,2187; 1728=12^3 and 2187=3^7
%e A128993 1764,4761; 1764=42^2 and 4761=69^2
%Y A128993 Cf. A117453.
%K A128993 nonn,base,tabf
%O A128993 1,1
%A A128993 _J. M. Bergot_, Apr 30 2007
%E A128993 Edited, and most terms replaced by _R. J. Mathar_, Nov 02 2009