
EXAMPLE

Denominators  Sum
+
2, 3, 4, 5, 6, 8, 9, 10, 15, 18, 20, 24  124
2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 28  126
2, 3, 4, 5, 6, 7, 9, 12, 14, 18, 20, 28  128
2, 3, 4, 5, 6, 8, 9, 10, 12, 18, 24, 30  131
2, 3, 4, 5, 6, 7, 8, 12, 14, 20, 24, 28  133


PROG

(Ruby)
def partition(n, min, max)
return [[]] if n == 0
[max, n].min.downto(min).flat_map{i partition(n  i, min, i  1).map{rest [i, *rest]}}
end
def f(n)
a = []
partition(n, 2, n).each{ary
sum = ary.inject(0){s, i s + 1 / i.to_r}
a << ary.reverse if sum.denominator == 1 && sum.numerator > 1
}
a
end
n = 1
a = []
while a == []
n += 1
a = f(n)
end
p a
