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

1,1

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

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

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

Cf. A242183, A242184, A242185.

Sequence in context: A307867 A099943 A118218 * A205189 A258695 A102562

Adjacent sequences: A242183 A242184 A242185 * A242187 A242188 A242189

Keyword

nonn

Author

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

Status

approved