# We have so much in common

Let $$S$$ be the set of all positive integers $$n$$ such that each of $$n$$ and $$n + 1$$ have exactly four divisors and have their divisors add to the same value.

Let $$m$$ be the number of elements in $$S$$ and $$b$$ be the sum of these $$m$$ elements.

Find $$m + b.$$

Inspired by Paul Ryan Longhas

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