# cabtaxi number

A 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 $a\geq b>0$ gives the definition for the taxicab numbers.

Title cabtaxi number CabtaxiNumber 2013-03-22 17:56:08 2013-03-22 17:56:08 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 00A08