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Search: id:A128993
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| A128993 |
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A table which contains in each row two or more perfect powers with the same digits. |
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1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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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
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CROSSREFS
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Cf. A117453.
Sequence in context: A059470 A141480 A155986 this_sequence A061450 A067974 A034290
Adjacent sequences: A128990 A128991 A128992 this_sequence A128994 A128995 A128996
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KEYWORD
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nonn,base,tabf,new
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Apr 30 2007
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EXTENSIONS
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Edited, and most terms replaced by R. J. Mathar - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 02 2009
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