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

1,2

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)).

Crossrefs

Cf. A072651, A072652.

Sequence in context: A227993 A072873 A361078 * A368107 A008478 A201009

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