Taxicab numbers are numbers that can be expressed in more than
one way as a sum of two positive cubes.
For example, the smallest taxicab number is 1729, since
Here the name taxicab is used in a somehow relaxed way. Other authors
define the th taxicab (or taxi-cab or Hardy-Ramanujan) number
as the smallest number that can be written in
different way as the sum two positive integral cubes.
The name(s) of these numbers derive from a famous anecdote involving
a taxicab and the famous mathematicians Hardy and Ramanujan (see the web pages linked below).
There are 870850 taxicab numbers up to .
The smallest one with 3 and 4 representations are
87539319 and 6963472309248.
The first taxicab numbers are
1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656 more terms
Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
A graph displaying how many taxicab numbers are multiples of the primes p
from 2 to 71. In black the ideal line 1/p