

A072653


Uniqued integer solutions n to n = b^c = c^d.


3



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
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OFFSET

1,2


COMMENTS

Numbers n such that (n^i)^(n^(1/i)) = (n^j)^(n^(1/j)) for some i and j.


LINKS

Table of n, a(n) for n=1..29.


FORMULA

See A072651 for calculation method.


EXAMPLE

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)).


MAPLE

a:=proc(N) local a, m, n; for m from 1 to N do for n from 1 to m1 do a:=(m/n)^((m*n)/(mn)); if(floor(a)=a)then print(a) fi; od; od; end: # convert into set # sort set  Giorgio Balzarotti and Paolo P. Lava, Nov 12 2005


CROSSREFS

Cf. A072651, A072652.
Sequence in context: A097764 A227993 A072873 * A008478 A201009 A111260
Adjacent sequences: A072650 A072651 A072652 * A072654 A072655 A072656


KEYWORD

nonn


AUTHOR

Henry Bottomley, Jun 28 2002


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Oct 07 2006, Jun 05 2007


STATUS

approved



