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%I #16 May 12 2014 12:08:14
%S 72,100,147,225,456,576,800,1050,1176,1539,1800,1944,2028,2645,2646,
%T 2695,2700,3025,3087,3275,3648,3844,3969,4335,4356,4500,4608,4950,
%U 5412,6000,6075,6400,7260,7623,8225,8400,8405,8450,8664,8820,9000,9408,9828,10108
%N Positive integers, c, such that there is more than one solution to the equation a^2 + b^3 = c^4, with a, b > 0.
%C 225, 1050, 1176, 2028, 3025, 6075, 7260, 8400, 8450, 8820, 9408, 10890, 12312, 18375, 19494, 21160, 24696, 26775, 28125, 28350, 31752, 31974, 34300, 39600, 43245, 44100, 49923, 53361, 54756, 58080, 64980, 67200, 71415, 75264, 87120, 98496, 131250, 139425, 144150, 145656, 159048, 164025, ... have three solutions;
%C 1800, 11025, 14400, 16224, 38025, 48600, 61347, 67600, 70560, 81675, 88200, 115200, 129792, 147000, 155952, 166419, ... have four solutions;
%C 24200, 77175, ... have five solutions.
%C A242192(a(n)) > 1. - _Reinhard Zumkeller_, May 07 2014
%H Lars Blomberg, <a href="/A242186/b242186.txt">Table of n, a(n) for n = 1..202</a>
%e 72 is in the sequence since 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
%t f[n_] := f[n] = Module[{a}, Array[(a = Sqrt[n^4 - #^3]; If[ IntegerQ@ a && a > 0, {a, #}, Sequence @@ {}]) &, Floor[n^(4/3)]]]; Select[ Range@ 10000, f@# > 1 &]
%o (Haskell)
%o a242186 n = a242186_list !! (n-1)
%o a242186_list = filter ((> 1) . a242192) [1..]
%o -- _Reinhard Zumkeller_, May 07 2014
%Y Cf. A242183, A242184, A242185.
%K nonn
%O 1,1
%A _Lars Blomberg_ and _Robert G. Wilson v_, May 06 2014