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%I #11 Nov 30 2016 05:15:28
%S 1036,1134,1352,1367,1430,1465,1484,1547,1582,1638,1709,1736,1764,
%T 1800,1801,1820,1862,1863,1881,1918,1953,1972,2009,2070,2080,2099,
%U 2136,2197,2268,2288,2305,2331,2340,2422,2464,2483,2485,2520,2548,2584,2799,2800
%N Numbers that are the sum of 4 distinct positive cubes in exactly 2 ways.
%H Jean-François Alcover, <a href="/A025409/b025409.txt">Table of n, a(n) for n = 1..439</a>
%e 1036 = 1^3 + 2^3 + 3^3 + 10^3 = 3^3 + 4^3 + 6^3 + 9^3.
%t Reap[For[n = 100, n <= 10000, n++, r = Reduce[0 < w < x < y < z && n == w^3 + x^3 + y^3 + z^3, {w, x, y, z}, Integers]; If[r =!= False, If[Length[r] == 2, Print[n]; Sow[n]]]]][[2, 1]] (* _Jean-François Alcover_, Nov 30 2016 *)
%K nonn
%O 1,1
%A _David W. Wilson_