Number of sums of factors
Brachylog, 8 bytes

{~×≜+}ᶜ¹


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Explanation

{    }ᶜ¹  Count unique results of this predicate:
 ~×       Create list of numbers whose product is the input.
   ≜      Label the list, forcing it to take a concrete value.
    +     Take its sum.


I'm not entirely sure why ~× only produces lists with elements above 1, but it seems to do so, which works great in this challenge.