# Big-O Notation

$$\sum_{p\leq N}\frac{1}{p}=\log\log N + A + O(\frac{1}{\log N})$$

Does it mean that we can simply replace the O part with a function that is a constant times 1/(log N)? What would be the difference between $$A + O(\frac{1}{\log N})$$ and $$O(1)$$?

shmoe
What would be the difference between $$A + O(\frac{1}{\log N})$$ and $$O(1)$$?