%I #19 Jun 01 2016 16:34:34

%S 36998208,449519625,2367885312,8016025680,9563569561,14753560033,

%T 26971693632,28769256000,61358997609,151544659968,225128651328,

%U 278450575201,282429583137,310289733000,310289733000,327699806625,498700534033,513025643520,578097000000

%N Values of A272701 that are the sum of a positive square and a positive cube in more than one way.

%C Taxi-cab numbers (A001235) that are the sum of two nonzero squares in more than one way and also the sum of a positive square and a positive cube in more than one way.

%C Subsequence of A273498.

%C A001235(293) = 6^3*A001235(16) = 6^3*171288 = 36998208 is the least number with this property.

%C 14753560033 = 1453*2677*3793 is the first term that is in A272935.

%C Obviously, in this sequence there are perfect powers infinitely many times.

%e 36998208 is a term because 36998208 = 102^3 + 330^3 = 144^3 + 324^3 = 1728^2 + 324^3 = 5832^2 + 144^3 = 648^2 + 6048^2 = 1728^2 + 5832^2.

%Y Cf. A001235, A007692, A054402, A272701, A273498.

%K nonn

%O 1,1

%A _Altug Alkan_, May 23 2016

%E a(2)-a(19) from _Giovanni Resta_, May 24 2016