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Lexicographically last solution to Erdős's Last Equation in n variables, x_1*...*x_n = n*(x_1 + ... + x_n), with 1 <= x_1 <= ... <= x_n, written as triangle T(n,k), 1<=k<=n.
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%I #8 Nov 08 2019 18:18:34

%S 1,4,4,3,3,3,2,2,2,6,1,1,3,5,5,1,1,2,3,3,5,1,1,1,2,3,3,7,1,1,2,2,2,2,

%T 2,4,1,1,1,1,2,3,3,3,3,1,1,1,1,1,2,2,2,3,10,1,1,1,1,1,1,1,3,3,3,11,1,

%U 1,1,1,1,1,1,2,2,3,4,6

%N Lexicographically last solution to Erdős's Last Equation in n variables, x_1*...*x_n = n*(x_1 + ... + x_n), with 1 <= x_1 <= ... <= x_n, written as triangle T(n,k), 1<=k<=n.

%C a(1) = T(1,1) = 1 assumed. Any number is a solution for n=1.

%D R. K. Guy, Sum equals product. in: Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, chapter D24, (2004), 299-301.

%H David A. Corneth, <a href="/A328910/a328910_1.gp.txt">list of solutions and product of variables of solutions for n = 2..160, omitting ones</a>.

%e The triangle begins:

%e 1;

%e 4, 4;

%e 3, 3, 3;

%e 2, 2, 2, 6;

%e 1, 1, 3, 5, 5;

%e 1, 1, 2, 3, 3, 5;

%e 1, 1, 1, 2, 3, 3, 7;

%e 1, 1, 2, 2, 2, 2, 2, 4;

%Y Cf. A328910, A328980, A329206.

%K nonn,tabl

%O 1,2

%A _Hugo Pfoertner_, Nov 08 2019