Composites with prime repunit property
A number consisting entirely of ones is called a repunit. We shall define R(k) to be a repunit of length k; for example, R(6) = 111111.
Given that n is a positive integer and GCD(n, 10) = 1, it can be shown that there always exists a value, k, for which R(k) is divisible by n, and let A(n) be the least such value of k; for example, A(7) = 6 and A(41) = 5.
You are given that for all primes, p > 5, that p − 1 is divisible by A(p). For example, when p = 41, A(41) = 5, and 40 is divisible by 5.
However, there are rare composite values for which this is also true; the first five examples being 91, 259, 451, 481, and 703.
Find the sum of the first twenty-five composite values of n for which
GCD(n, 10) = 1 and n − 1 is divisible by A(n).
只包含数字1的数被称为循环单位数，我们定义R(k)是长为k的循环单位数，例如，R(6) = 111111。
如果n是一个整数，且GCD(n, 10) = 1，可以验证总存在k使得R(k)能够被n整除，并且记A(n)是这些k中最小的一个。例如，A(7) = 6，而A(41) = 5。
已知对于素数p > 5，p − 1能够被A(p)整除。例如，当p = 41时，A(41) = 5，而40能够被5整除。
GCD(n, 10) = 1且n − 1能够被A(n)整除，并求它们的和。