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# Problem 565

Divisibility of sum of divisors

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