Dirichlet convolution with multiplicative function

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$$μ * 1 = e$$
$$φ * 1 = id \Rightarrow φ = μ * id$$
$$d = 1* 1 \Rightarrow 1 = μ * d$$
among them:
$$\sum_{d|n} μ(d) = {[n==1]}$$
$$\sum_{d|n} φ(d) = {n}$$
$$\sum_{d|n} μ(n/d)*d = {φ(n)}$$
$$\sum_{d|n} μ(n/d)*d = {φ(n)}$$
$$d(i,j) = \sum_{p|i} \sum_{q|j} [gcd(p,q)=1]$$