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%I #29 Aug 29 2020 09:24:38
%S 1,14,70993724
%N Smallest possible largest number in a set of n integers such that the sum of any two numbers is a positive cube.
%C Here, the smallest number is negative (since we need the smallest such largest number) and the remaining numbers are positive (since the condition is about positive cubes).
%H Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/1010.html">Problem of the month October 2010</a>
%H Andrzej Nowicki, <a href="http://www-users.mat.umk.pl/~anow/imperium/szb02.pdf">Podroze po Imperium Liczb</a> [broken link]
%e { -35780, 4693243, 11888132, 70993724 } is the smallest set of 4 numbers such that all 6 combinations of sum of any two numbers is a perfect cube. For example, -35780 + 70993724 = 414^3 and 4693243 + 11888132 = 255^3.
%e { -13, 13, 14 } is the smallest set of 3 numbers where all 3 combinations of sum of any two numbers is a perfect cube.
%e { -1, 1 } is the trivial set of two numbers because -1 + 1 = 0^3.
%Y Cf. A000578, A195854, A195899.
%K nonn,more,bref
%O 2,2
%A _Kausthub Gudipati_, Sep 25 2011
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