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

125, 512, 144, 441, 169, 196, 961, 243, 324, 256, 625, 1024, 2401, 1089, 9801, 1296, 2916, 9216, 1369, 1936, 1728, 2187, 1764, 4761, 2197, 7921, 4096, 9604, 10201, 12100, 10404, 14400, 40401, 44100, 10609, 16900, 19600, 61009, 90601, 96100

Offset: 1

Author

J. M. Bergot, Apr 30 2007

Keywords

• nonn
• base
• tabf

Comments

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.

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.

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

Examples

			The table starts with the first 11 rows as follows:
125,512; 125=5^3 and 512 = 2^9 = 8^3
144,441; 144=12^2 and 441=21^2
169,196,961; 169=13^2 and 196=14^2 and 961=31^2
243,324; 243=3^5 and 324=18^2
256,625; 256 = 16^2=4^4 and 625=25^2=5^4
1024,2401; 1024=2^10=32^2 and 2401=49^2=7^4
1089,9801; 1089=33^2 and 9801=99^2
1296,2916,9216; 1296=36^2 and 2916=54^2 and 9216=96^2
1369,1936; 1369=37^2 and 1936=44^2
1728,2187; 1728=12^3 and 2187=3^7
1764,4761; 1764=42^2 and 4761=69^2
		

Crossrefs

Cf. A117453.

Extensions

Edited, and most terms replaced by R. J. Mathar, Nov 02 2009