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Search: id:A072653
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| A072653 |
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Uniqued integer solutions n to n = b^c=c^d. |
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+0
4
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| 1, 4, 16, 27, 64, 256, 729, 1024, 3125, 4096, 16384, 19683, 46656, 65536, 262144, 531441, 823543, 1048576, 4194304, 9765625, 14348907, 16777216, 67108864, 268435456, 387420489, 1073741824, 2176782336, 4294967296, 10000000000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers n such that (n^i)^(n^(1/i))=(n^j)^(n^(1/j)) for some i and j.
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FORMULA
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See A072651 for calculation method.
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EXAMPLE
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1 is included because of solutions of the form b^0=0^0, 1^c=c^0 and 1^1=1^d; 4 since 2^2=2^2; 16 since 2^4=4^2 and 4^2=2^4; 27 since 3^3=3^3; 64 since 8^2=2^6; etc.
The 10th element is n = 4096 with i = 12 and j = 6 because (4096^12)^(4096^(1/12)) = (4096^6)^(4096^(1/6))
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MAPLE
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a:=proc(N) local a, m, n; for m from 1 to N do for n from 1 to m-1 do a:=(m/n)^((m*n)/(m-n)); if(floor(a)=a)then print(a) fi; od; od; end: # convert into set # sort set - Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Nov 12 2005
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CROSSREFS
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Cf. A072651, A072652,
Sequence in context: A134330 A097764 A072873 this_sequence A008478 A137231 A111260
Adjacent sequences: A072650 A072651 A072652 this_sequence A072654 A072655 A072656
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jun 28 2002
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EXTENSIONS
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Edited by njas at the suggestion of Andrew Plewe, Oct 07 2006, Jun 05 2007
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