Each divisor of n looks like p₁ⁱ × p₂^j. The sum on the right is

(φ(p₁^a) + p₁ + p₁² + p₁³ + ... + p₁^a) × (φ(p₂^b) + p₂ + p₂² + p₂³ + ... + p₂^b)

Using CRT you can make a bijection between terms on the right and and i on the left. For example, there are φ(n) values for which gcd(i, n) = 1, and there is φ(p₁^a)φ(p₂^b) = φ(n) on the right. Also, you can take φ(p₁^a) values which are coprime to p and then you can take only one of p₂, p₂², ... to make i for which gcd(i, n) = p₂, or p₂², etc.