--description--

Let $g(n)$ be a sequence defined as follows:

$$\begin{align} & g(4) = 13, \\ & g(n) = g(n-1) + gcd(n, g(n - 1)) \text{ for } n > 4. \end{align}$$

The first few values are:

$$\begin{array}{l} n & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & \ldots \\ g(n) & 13 & 14 & 16 & 17 & 18 & 27 & 28 & 29 & 30 & 31 & 32 & 33 & 34 & 51 & 54 & 55 & 60 & \ldots \end{array}$$

You are given that $g(1\,000) = 2\,524$ and $g(1\,000\,000) = 2\,624\,152$.

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

--hints--

gcdSequence() should return 2744233049300770.

assert.strictEqual(gcdSequence(), 2744233049300770);

--seed--

--seed-contents--

function gcdSequence() {

  return true;
}

gcdSequence();

--solutions--

// solution required