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443. 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:

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

Find g(10¹⁵).