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# Problem 377

Sum of digits, experience 13

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

5、14、23、32、41、113、122、131、212、221、311、1112、1121、1211、2111和11111。