The sum of the positive divisors of is . Find the sum of the reciprocals of the positive divisors of .
Source: NCTM Mathematics Teacher, February 2008
Given that , the number of divisors is . The first twelve divisors are small and easy to guess: , and and as a bonus we get the last twelve by dividing by the first twelve divisors. For example, , etc. : .
When we add the reciprocals of the divisors, the divisors appear as denominators in a set of 24 fractions
When we reduce the fractions to (the least common denominator), the divisors appear as numerators