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.

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

Author

Lars Blomberg and Robert G. Wilson v, May 06 2014

Keywords

• nonn

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

Examples

			72 is in the sequence since 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..202

Crossrefs

Cf. A242183, A242184, A242185.

Programs

Haskell

a242186 n = a242186_list !! (n-1)
a242186_list = filter ((> 1) . a242192) [1..]
-- Reinhard Zumkeller, May 07 2014

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 &]