The Optimal Pairs

For two positive integers $a$ and $b$, let $g(a, b) =$ [gcd](https://en.wikipedia.org/wiki/Greatest_common_divisor) $(a, b) +$ [lcm](https://en.wikipedia.org/wiki/Least_common_multiple)$(a, b)$. For a positive integer $N$, let $f(N)$ denote the **minimum** value of $g(a, b)$ over all the pairs of positive integers $(a, b)$ such that $a+b = N$. Find out the number of **ordered** pairs $(a, b)$ s