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%I A273753 #21 Feb 23 2017 22:04:58
%S A273753 6742008,53936064,182034216,431488512,842751000,1456273728,1581292125,
%T A273753 2312508744,3451908096,4914923832,6742008000,8973612648,11395366632,
%U A273753 11650189824,12650337000,14812191576,18500069952,22754277000,27615264768,33123485304,39319390656
%N A273753 Taxi-cab numbers (A001235) that are the average of two positive cubes in more than one way.
%C A273753 Motivation for this sequence is that question: What is the least odd term of this sequence?
%C A273753 1581292125 = 3^6*5^3*7*37*67 is the least odd number that is the term of this sequence.
%H A273753 Chai Wah Wu, <a href="/A273753/b273753.txt">Table of n, a(n) for n = 1..64</a>
%e A273753 6742008 is a term because 6742008 = 46^3 + 188^3 = 126^3 + 168^3 = (14^3 + 238^3)/2 = (105^3 + 231^3)/2.
%e A273753 53936064 is a term because 53936064 = 2^3*6742008.
%e A273753 1581292125 is a term because 1581292125 = 50^3 + 1165^3 = 540^3 + 1125^3 = (435^3 + 1455^3)/2 = (909^3 + 1341^3)/2.
%o A273753 (PARI) T = thueinit(x^3+1, 1);
%o A273753 isA001235(n) = my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1;
%o A273753 isok(n) = isA001235(n) && isA001235(2*n);
%Y A273753 Cf. A001235, A191345.
%K A273753 nonn
%O A273753 1,1
%A A273753 _Altug Alkan_, May 29 2016
%E A273753 a(5)-a(21) from _Giovanni Resta_, Jun 01 2016

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