A242192 Number of ways to write n^4 as sum of a square and a cube, both > 0.

0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Reinhard Zumkeller, May 07 2014

Keywords

• nonn

Comments

a(n) = number of occurrences of n in A242183;

a(A242186(n)) > 1.

Examples

			a(6) = #{28^2 + 8^3} = 1;
a(72) = #{4941^2 + 135^3, 1728^2 + 288^3} = 2;
a(225) = #{49375^2 + 500^3, 33750^2 + 1125^3, 10125^2 + 1350^3} = 3;
a(1800) = #{3160000^2 + 8000^3, 2835000^2 + 13500^3, 2160000^2 + 18000^3, 648000^2 + 21600^3} = 4;
a(24200) = #{582914112^2 + 147136^3, 564344000^2 + 290400^3, 479160000^2 + 484000^3, 219615000^2 + 665500^3, 42092875^2 + 698775^3} = 5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010052, A000578, A000583.

Programs

Haskell

a242192 n = sum $ map (a010052 . (n ^ 4 -)) $
                      takeWhile (< n ^ 4) $ map (^ 3) [1..]
-- Reinhard Zumkeller, May 07 2014