login
Ordered solutions greater than 1 to b^c=c^d, with multiplicity.
3

%I #3 Mar 30 2012 18:51:38

%S 4,16,16,27,64,256,256,729,1024,3125,4096,4096,16384,19683,46656,

%T 65536,65536,65536,262144,531441,823543,1048576,1048576,4194304,

%U 9765625,14348907,16777216,16777216,16777216,67108864,268435456,268435456

%N Ordered solutions greater than 1 to b^c=c^d, with multiplicity.

%C There are also infinite numbers of solutions giving 1, of the forms b^0=0^0, 1^c=c^0 and 1^1=1^d.

%F See A072651 for calculation method.

%e 65536 appears three times because 256^2=2^16, 2^16=16^4 and 16^4=4^8 are all solutions, each coming to 65536.

%Y Cf. A072651, A072653.

%K nonn

%O 2,1

%A _Henry Bottomley_, Jun 28 2002