Digit Sum Division (noch nicht übersetzt)

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 F(N)=Nn=1nd(n).

You are given F(10)=19, F(123)1.187764610390e3 and F(12345)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.