MathDB

Let

S_n

be the sum of reciprocal values of non-zero digits of all positive integers up to (and including)

n

. For instance,

S_{13} = \frac{1}{1}+ \frac{1}{2}+ \frac{1}{3}+ \frac{1}{4}+ \frac{1}{5}+ \frac{1}{6}+ \frac{1}{7}+ \frac{1}{8}+ \frac{1}{9}+ \frac{1}{1}+ \frac{1}{1}+ \frac{1}{1}+ \frac{1}{1}+ \frac{1}{2}+ \frac{1}{1}+ \frac{1}{3}

. Find the least positive integer

k

making the number

k!\cdot S_{2016}

an integer.

Problem Statement