## Gozinta Chains

### Problem 548

A **gozinta chain **for `n` is a sequence {1,a,b,...,`n`} where each element properly divides the next.

There are eight gozinta chains for 12:

{1,12} ,{1,2,12}, {1,2,4,12}, {1,2,6,12}, {1,3,12}, {1,3,6,12}, {1,4,12} and {1,6,12}.

Let g(`n`) be the number of gozinta chains for `n`, so g(12)=8.

g(48)=48 and g(120)=132.

Find the sum of the numbers `n` not exceeding 10^{16} for which g(`n`)=`n`.