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

%I #4 May 07 2014 03:12:02

%S 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,

%T 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,

%U 0,0,1,2,0,0,1,0,0,1,0,0,0,0,0,0,0,0

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

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

%C a(A242186(n)) > 1.

%H Reinhard Zumkeller, <a href="/A242192/b242192.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6) = #{28^2 + 8^3} = 1;

%e a(72) = #{4941^2 + 135^3, 1728^2 + 288^3} = 2;

%e a(225) = #{49375^2 + 500^3, 33750^2 + 1125^3, 10125^2 + 1350^3} = 3;

%e a(1800) = #{3160000^2 + 8000^3, 2835000^2 + 13500^3, 2160000^2 + 18000^3, 648000^2 + 21600^3} = 4;

%e a(24200) = #{582914112^2 + 147136^3, 564344000^2 + 290400^3, 479160000^2 + 484000^3, 219615000^2 + 665500^3, 42092875^2 + 698775^3} = 5.

%o (Haskell)

%o a242192 n = sum $ map (a010052 . (n ^ 4 -)) $

%o takeWhile (< n ^ 4) $ map (^ 3) [1..]

%o -- _Reinhard Zumkeller_, May 07 2014

%Y Cf. A010052, A000578, A000583.

%K nonn

%O 1,72

%A _Reinhard Zumkeller_, May 07 2014