Definition:Hardy-Ramanujan Number

Definition
The $n$th Hardy-Ramanujan number $\operatorname {Ta} \left({n}\right)$ is the smallest positive integer which can be expressed as the sum of $2$ cubes in $n$ different ways.

Also known as
The Hardy-Ramanujan numbers are also (more commonly) known as taxicab numbers from the often-cited anecdote of 's visit to in hospital.

Hence the usual denotation of the $n$th such number: $\operatorname {Ta} \left({n}\right)$; Ta for taxicab.

However, the name taxicab number is ambiguous; it is also defined (with exactly the same nomenclative derivation) as the sequence of numbers expressible as the sum of $2$ positivecubes.

Because of that ambiguity, the term Hardy-Ramanujan numbers is to be used on in preference.

Also see

 * Definition:Taxicab Number