--description--

There are 16 positive integers that do not have a zero in their digits and that have a digital sum equal to 5, namely:

5, 14, 23, 32, 41, 113, 122, 131, 212, 221, 311, 1112, 1121, 1211, 2111 and 11111.

Their sum is 17891.

Let $f(n)$ be the sum of all positive integers that do not have a zero in their digits and have a digital sum equal to $n$.

Find $\displaystyle\sum_{i=1}^{17} f(13^i)$. Give the last 9 digits as your answer.

--hints--

experience13() should return 732385277.

assert.strictEqual(experience13(), 732385277);

--seed--

--seed-contents--

function experience13() {

  return true;
}

experience13();

--solutions--

// solution required