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%I #22 Apr 26 2016 21:33:01
%S 75,87,126,135,150,171,174,204,225,246,252,261,270,297,300,333,342,
%T 348,375,378,405,408,435,450,457,492,504,513,522,525,540,543,594,600,
%U 609,612,618,630,645,666,675,684,696,723,738,741,750,753,756,783,788,810,813,815,816,825,855,870,882,891,900,914
%N Numbers n such that n^3 = (x^3 + y^3 + z^3) / 3 where x > y > z > 0, is soluble.
%C Numbers whose cube is the average of three distinct positive cubes.
%C If n is in this sequence, then k*n is also a member of this sequence for all k > 0.
%C Terms that are not divisible by 3 are 457, 788, 815, 914, ...
%C Terms that are not members of A023042 are 457, 914, 1078, ...
%H Chai Wah Wu, <a href="/A272023/b272023.txt">Table of n, a(n) for n = 1..1000</a>
%e 75 is a term because 75^3 = (10^3 + 17^3 + 108^3) / 3.
%e 150 = 2*75 is a term.
%e 87 is a term because 87^3 = (13^3 + 54^3 + 122^3) / 3.
%e 457 is a term because 457^3 = (226^3 + 379^3 + 604^3) / 3.
%Y Cf. A023042, A024975.
%K nonn
%O 1,1
%A _Altug Alkan_, Apr 18 2016