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A242186 Positive integers, c, such that there is more than one solution to the equation a^2 + b^3 = c^4, with a, b > 0.

%I A242186 #16 May 12 2014 12:08:14
%S A242186 72,100,147,225,456,576,800,1050,1176,1539,1800,1944,2028,2645,2646,
%T A242186 2695,2700,3025,3087,3275,3648,3844,3969,4335,4356,4500,4608,4950,
%U A242186 5412,6000,6075,6400,7260,7623,8225,8400,8405,8450,8664,8820,9000,9408,9828,10108
%N A242186 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 A242186 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 A242186 1800, 11025, 14400, 16224, 38025, 48600, 61347, 67600, 70560, 81675, 88200, 115200, 129792, 147000, 155952, 166419, ... have four solutions;
%C A242186 24200, 77175, ... have five solutions.
%C A242186 A242192(a(n)) > 1. - _Reinhard Zumkeller_, May 07 2014
%H A242186 Lars Blomberg, <a href="/A242186/b242186.txt">Table of n, a(n) for n = 1..202</a>
%e A242186 72 is in the sequence since 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
%t A242186 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 A242186 (Haskell)
%o A242186 a242186 n = a242186_list !! (n-1)
%o A242186 a242186_list = filter ((> 1) . a242192) [1..]
%o A242186 -- _Reinhard Zumkeller_, May 07 2014
%Y A242186 Cf. A242183, A242184, A242185.
%K A242186 nonn
%O A242186 1,1
%A A242186 _Lars Blomberg_ and _Robert G. Wilson v_, May 06 2014