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Find all positive integers

k

that can be expressed as the sum of

50

fractions such that the numerators are the

50

natural numbers from

1

50

and the denominators are positive integers, that is,

k = \dfrac{1}{a_1} + \dfrac{2}{a_2} + \ldots + \dfrac{50}{a_{50}}

with a

_1 , a_2 , \ldots , a_n

positive integers.

Problem Statement