Parity of Power-Sum Divisors

For a positive integer $n$, we define $s_{26}(n)$ to be the sum of the 26th powers of all the positive proper (i.e., not including $n$) divisors of $n$. That is, $$s_{26}(n) = \sum_{d\mid n,\ d\neq n} d^{26}.$$ For how many integers $2\le n\le 100$ is $s_{26}(n)$ odd?