cabtaxi number

A cabtaxi number for a given $n$ is the smallest positive number which can be written as $a^3+b^3$ in $n$ different ways, with either $a$ or $b$ allowed to be negative integers. For example, 91 is the 2nd cabtaxi number since it can be expressed ${(-5)}^3+6^3=3^3+4^3=91$. The known cabtaxi numbers are 1, 91, 728, 2741256, 6017193, 1412774811, 11302198488, 137513849003496, 424910390480793000, listed in A047696 of Sloane’s OEIS. Adding the restriction $a\ge b>0$ gives the definition for the taxicab numbers.

Title	cabtaxi number
Canonical name	CabtaxiNumber
Date of creation	2013-03-22 17:56:08
Last modified on	2013-03-22 17:56:08
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 00A08