Definition:Hardy-Ramanujan Number/Historical Note

Historical Note on Hardy-Ramanujan Number

The anecdote related by G.H. Hardy about a visit to Srinivasa Ramanujan in hospital in a taxicab whose number was $1729$ is well-known and often repeated.

The concept was first introduced by Bernard Frénicle de Bessy in $1657$, who discovered $5$ instances of these numbers, including $1729$, in response to a challenge by Leonhard Paul Euler.

Those are the numbers referred to as taxicab numbers on $\mathsf{Pr} \infty \mathsf{fWiki}$, following the lead of N.J.A. Sloane on the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

However, the deeper concept of the Hardy-Ramanujan numbers is more recent.

After $1729$, the next Hardy-Ramanujan number $\operatorname {Ta} \left({3}\right)$ was discovered by John Leech in $1957$ to be $87 \, 539 \, 319$.

Sources

• Weisstein, Eric W. "Taxicab Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TaxicabNumber.html