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7, 13, 31, 37, 31, 73, 79, 103, 103, 109, 103, 193, 139, 181, 211, 193, 331, 373, 349, 421, 541, 421, 439, 601, 883, 613, 673, 769, 883, 631, 1153, 787, 739, 733, 1063, 1033, 1291, 1279, 853, 1009, 1801, 1231, 1951, 1153, 1531, 1453, 997, 1693
EXAMPLE
a(1) = 7 because A272935(1) = 1729 and 1729 = 7*13*19.
Values of A272701 that are the sum of a positive square and a positive cube in more than one way.
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36998208, 449519625, 2367885312, 8016025680, 9563569561, 14753560033, 26971693632, 28769256000, 61358997609, 151544659968, 225128651328, 278450575201, 282429583137, 310289733000, 310289733000, 327699806625, 498700534033, 513025643520, 578097000000
COMMENTS
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. A001235(293) = 6^3* A001235(16) = 6^3*171288 = 36998208 is the least number with this property.
14753560033 = 1453*2677*3793 is the first term that is in A272935. Obviously, in this sequence there are perfect powers infinitely many times.
EXAMPLE
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.
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