Eccoci.

Let $\sigma (n)$ be the sum of the divisors of $n$.
E.g. the divisors of $4$ are $1$, $2$ and $4$, so $\sigma (4)=7$.

The numbers $n$ not exceeding $20$ such that $7$ divides $\sigma (n)$ are: $4$, $12$, $13$ and $20$, the sum of these numbers being $49$.

Let $S(n,d)$ be the sum of the numbers $i$ not exceeding $n$ such that $d$ divides $\sigma (i)$.
So $S(20,7)=49$.

You are given: $S({10}^6,2017)=150850429$ and $S({10}^9,2017)=249652238344557$.

Find $S({10}^{11},2017)$.