Digit Sum Division (noch nicht ├╝bersetzt)

Problem 776

For a positive integer $n$, $d(n)$ is defined to be the sum of the digits of $n$. For example, $d(12345)=15$.

Let $\displaystyle F(N)=\sum_{n=1}^N \frac n{d(n)}$.

You are given $F(10)=19$, $F(123)\approx 1.187764610390e3$ and $F(12345)\approx 4.855801996238e6$.

Find $F(1234567890123456789)$. Write your answer in scientific notation rounded to twelve significant digits after the decimal point. Use a lowercase e to separate the mantissa and the exponent.