The strict inequality between dismal divisor counts and their sum

Let $d_{10}(n)$ denote the number of dismal divisors of $n$ in base $10$, and let $\sigma_{10}(n)$ denote the dismal sum of those divisors. Dismal divisor-sum inequality. For every integer $n>1$,

$$d_{10}(n)<\sigma_{10}(n).$$

The conjecture compares the number of dismal divisors with their dismal sum. It is presented as an unresolved conjecture at the end of the section, with no proof or resolution given.