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Integers expressible in at least two ways as a^3 + b^4, where a,b > 0.
2

%I #16 Sep 27 2012 20:45:24

%S 4097,10729,15641,175625,195193,408536,531442,535537,549017,831209,

%T 852984,883664,1778625,3185784,4258089,5555233,8876304,11338448,

%U 11402289,12721424,13844736,16777217,16781312,17182440,17308657,19169848,19703736,22667633,26248698

%N Integers expressible in at least two ways as a^3 + b^4, where a,b > 0.

%C Numbers are listed in increasing order, no duplicates allowed (i.e., if the number is so expressible in 3 or more ways).

%C a(n) >> n^(12/7) by a counting argument. Can this be improved? Is there a corresponding upper bound? - _Charles R Greathouse IV_, Sep 27 2012

%H Frank Ruskey, <a href="/A217196/b217196.txt">Table of n, a(n) for n = 1..5000</a>

%e a(1) = 4097 = 1^3 + 8^4 = 16^3 + 1^4 is the smallest such number.

%K nonn

%O 1,1

%A _Frank Ruskey_, Sep 27 2012