# Problem 417: Reciprocal cycles II

![graphic](img417.gif)

A unit fraction contains 1 in the numerator. The decimal representation
of the unit fractions with denominators 2 to 10 are given: 1/2= 0.5
1/3= 0.(3) 1/4= 0.25 1/5= 0.2 1/6= 0.1(6) 1/7= 0.(142857) 1/8= 0.125
1/9= 0.(1) 1/10= 0.1 Where 0.1(6) means 0.166666..., and has a 1-digit
recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Unit fractions whose denominator has no other prime factors than 2
and/or 5 are not considered to have a recurring cycle. We define the
length of the recurring cycle of those unit fractions as 0. Let L(n)
denote the length of the recurring cycle of 1/n. You are given that
∑L(n) for 3 ≤ n ≤ 1 000 000 equals 55535191115. Find ∑L(n) for 3 ≤ n ≤
100 000 000