A, B and C are polynomial increasing sequences of positive integers.

1. A(k) + B(k) = C(k)
2. A(8) is a square
3. C(8)= 128.
Both A and B series have only one prime number as a member.
Each member of C is evenly divisible by at least one square (other than 1) number.

How are the sequences A, B and C defined?
What's so special about them?