Let S_{n} be the sum of the reciprocals of the nonzero digits of the integers from 1 to 10^{n}, inclusive.
Find the smallest positive integer n for which S_{n} is an integer.
Let S_{n} be the sum of the reciprocals of the nonzero digits of the integers from 1 to 10^{n}, inclusive.
Find the smallest positive integer n for which S_{n} is an integer.