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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 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.)