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

单词	CabtaxiNumber
释义	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 $a\\geq b>0$ gives the definition for the taxicab numbers.
随便看	Halley’s formula HallsMarriageTheorem HallsMarriageTheoremProofOf HallSubgroup Hall subgroup Hall’s marriage theorem Hall’s marriage theorem, proof of HaltingProblem halting problem HamelFunction Hamel function HamiltonEquations Hamilton equations HamiltonianAlgebroids Hamiltonian algebroids HamiltonianCycle Hamiltonian cycle HamiltonianGraph Hamiltonian graph HamiltonianGroup Hamiltonian group HamiltonianOperator Hamiltonian operator HamiltonianPath Hamiltonian path