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%I A018850 #33 Jul 27 2020 04:51:20
%S A018850 1729,4104,20683,39312,40033,64232,65728,134379,149389,171288,195841,
%T A018850 216027,327763,402597,439101,443889,515375,684019,704977,805688,
%U A018850 842751,920673,955016,984067,994688,1009736,1016496,1073375,1092728,1331064
%N A018850 Numbers that are the sum of 2 cubes in more than 1 way (primitive solutions).
%C A018850 Nakao's table has more entries because he lists nonprimitive numbers if they are the sum of two cubes in three ways.
%C A018850 _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)).
%H A018850 Shahar Amitai, <a href="/A018850/b018850.txt">Table of n, a(n) for n = 1..9859</a> (terms a(1)-a(1694) from T. D. Noe).
%H A018850 Shahar Amitai, <a href="/A018850/a018850.txt">Python code to generate all primitive taxicab numbers up to N.</a>
%H A018850 H. Nakao, <a href="http://www.kaynet.or.jp/~kay/misc/log/rtaxi.log">Ramanujan Taxi Numbers [1...1000000000]</a>
%H A018850 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%Y A018850 Cf. A001235.
%K A018850 nonn
%O A018850 1,1
%A A018850 _David W. Wilson_

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