A242183 Integers c, listed with multiplicity, such that there is a solution to the equation a^2 + b^3 = c^4, with integers a, b > 0.

6, 9, 15, 35, 36, 42, 48, 57, 63, 71, 72, 72, 75, 78, 90, 98, 100, 100, 120, 135, 141, 147, 147, 162, 195, 196, 204, 208, 215, 225, 225, 225, 243, 252, 260, 279, 280, 288, 289, 295, 300, 306, 336, 363, 364, 384, 405, 441, 450, 456, 456, 462, 504, 510, 525, 537

Offset: 1

Author

Lars Blomberg, May 06 2014

Keywords

• nonn

Comments

A242192(k) gives number of occurrences of k. - Reinhard Zumkeller, May 07 2014

See A300564 for the list of values without duplicates. - M. F. Hasler, Apr 16 2018

Examples

			6 is in the sequence because 6^4 = 28^2 + 8^3.
72 is in the sequence twice because 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
		

Links

• Lars Blomberg, Table of n, a(n) for n = 1..2241

Crossrefs

Cf. A242184, A242185, A242186.

Programs

Haskell

a242183 n = a242183_list !! (n-1)
a242183_list = concatMap (\(r,x) -> take r [x,x..]) $
                         zip a242192_list [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)]]];; k = 1; lst = {}; While[k < 3001, If[ f[k] != {}, AppendTo[lst, k]; Print[{k, f[k]}]]; k++]; s = Select[ Range[3000], f@# != {} &]; l = Length@ f@ # & /@ s; Flatten[ Table[ s[[#]], {l[[#]]}] & /@ Range@ Length@ s] (* Robert G. Wilson v, May 06 2014 *)

Formula

c = sqrt(sqrt(a^2+b^3)) is an integer.