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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.
6
72, 100, 147, 225, 456, 576, 800, 1050, 1176, 1539, 1800, 1944, 2028, 2645, 2646, 2695, 2700, 3025, 3087, 3275, 3648, 3844, 3969, 4335, 4356, 4500, 4608, 4950, 5412, 6000, 6075, 6400, 7260, 7623, 8225, 8400, 8405, 8450, 8664, 8820, 9000, 9408, 9828, 10108
OFFSET
1,1
COMMENTS
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;
1800, 11025, 14400, 16224, 38025, 48600, 61347, 67600, 70560, 81675, 88200, 115200, 129792, 147000, 155952, 166419, ... have four solutions;
24200, 77175, ... have five solutions.
A242192(a(n)) > 1. - Reinhard Zumkeller, May 07 2014
LINKS
EXAMPLE
72 is in the sequence since 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
MATHEMATICA
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 &]
PROG
(Haskell)
a242186 n = a242186_list !! (n-1)
a242186_list = filter ((> 1) . a242192) [1..]
-- Reinhard Zumkeller, May 07 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved