Explain the last term in the sum in Theorem. Why is | A  B  C | added and | B  C | subtrac...

Explain the last term in the sum in Theorem. Why is | A  B  C | added and | B  C | subtracted?

Theorem

Every positive integer n >1 can be written uniquely as  where p1 < p2< • • • < ps are distinct primes that divide n and the k’s are positive integers giving the number of times each prime occurs as a factor of n.