A072653 Uniqued integer solutions n to n = b^c = c^d.

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

Offset: 1

Author

Henry Bottomley, Jun 28 2002

Keywords

• nonn

Comments

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

Examples

			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)).
		

Crossrefs

Cf. A072651, A072652.

Formula

See A072651 for calculation method.

Extensions

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