A018850 Numbers that are the sum of 2 cubes in more than 1 way (primitive solutions).

1729, 4104, 20683, 39312, 40033, 64232, 65728, 134379, 149389, 171288, 195841, 216027, 327763, 402597, 439101, 443889, 515375, 684019, 704977, 805688, 842751, 920673, 955016, 984067, 994688, 1009736, 1016496, 1073375, 1092728, 1331064

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Nakao's table has more entries because he lists nonprimitive numbers if they are the sum of two cubes in three ways.

Rajesh Bhowmick, Dec 12 2011: The odd number 40533595075161 can be represented as sum of two cubes in just two different ways: (34314)^(3)+(5073)^(3) = (34321)^(3)+(4730)^(3). Here, the cubes are greater than 1, there is no common factor between the odd numbers, there is no common factor between the L.H.S & the R.H.S, the even number is greater than 2, the cubes are in their primitive form, and they are not of the form (27)^(3) or (121)^(3) (which are actually (3)^(9) & (11)^(6)).

Links

• Shahar Amitai, Table of n, a(n) for n = 1..9859 (terms a(1)-a(1694) from T. D. Noe).
• Shahar Amitai, Python code to generate all primitive taxicab numbers up to N.
• H. Nakao, Ramanujan Taxi Numbers [1...1000000000]
• Eric Weisstein's World of Mathematics, Cubic Number

Crossrefs

Cf. A001235.