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

%I A242192 #4 May 07 2014 03:12:02
%S A242192 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 A242192 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 A242192 0,0,1,2,0,0,1,0,0,1,0,0,0,0,0,0,0,0
%N A242192 Number of ways to write n^4 as sum of a square and a cube, both > 0.
%C A242192 a(n) = number of occurrences of n in A242183;
%C A242192 a(A242186(n)) > 1.
%H A242192 Reinhard Zumkeller, <a href="/A242192/b242192.txt">Table of n, a(n) for n = 1..10000</a>
%e A242192 a(6) = #{28^2 + 8^3} = 1;
%e A242192 a(72) = #{4941^2 + 135^3, 1728^2 + 288^3} = 2;
%e A242192 a(225) = #{49375^2 + 500^3, 33750^2 + 1125^3, 10125^2 + 1350^3} = 3;
%e A242192 a(1800) = #{3160000^2 + 8000^3, 2835000^2 + 13500^3, 2160000^2 + 18000^3, 648000^2 + 21600^3} = 4;
%e A242192 a(24200) = #{582914112^2 + 147136^3, 564344000^2 + 290400^3, 479160000^2 + 484000^3, 219615000^2 + 665500^3, 42092875^2 + 698775^3} = 5.
%o A242192 (Haskell)
%o A242192 a242192 n = sum $ map (a010052 . (n ^ 4 -)) $
%o A242192                       takeWhile (< n ^ 4) $ map (^ 3) [1..]
%o A242192 -- _Reinhard Zumkeller_, May 07 2014
%Y A242192 Cf. A010052, A000578, A000583.
%K A242192 nonn
%O A242192 1,72
%A A242192 _Reinhard Zumkeller_, May 07 2014