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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 (list; graph; refs; listen; history; text; internal format)
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 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, 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

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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)