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 $g(1000)=2524$ and $g(1000000)=2624152$.

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