What does the notation $\sum_{d\mid (k,n)}$ mean

Question

I'm trying to understand how to generate this sequence, but I'm confused about this notation:

$$\sum_{d\mid (k,n)}$$

Does it mean the sum of all factors of both $k$ and $n$?

Answer 1

A sum of the form $$\sum_{d \mid n}$$ is a sum where $d$ takes all the positive divisors of $n$.

The notation $(k,n)$ is often used to represent $\gcd(k,n)$, the greatest common divisor of $k$ and $n$.

So $$\sum_{d \mid (k,n)}$$ mean that the sum is taken over all the positive divisors of $(k, n)$.

Note that been a divisor of $(k,n)$ is the same as been a divisor of both $k$ and $n$.