GCD sequence

Let $g(n)$ be a sequence defined as follows: $g(4) = 13$, $g(n) = g(n-1) + gcd(n, g(n-1))$ for $n > 4$.

The first few values are:

n 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ... g(n) 13 14 16 17 18 27 28 29 30 31 32 33 34 51 54 55 60 ...

You are given that $g(1\ 000) = 2524$ and $g(1\ 000\ 000) = 2624152$.

Find $g(10^{15})$.