常用积性函数替换
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<pre><code class="language-markdown">$$
n = \sum_{d|n}\varphi(d)\ \ <==>\ \ id = \varphi*I
$$
$$
\frac{\varphi(n)}{n} = \sum_{d|n}\frac{\mu(d)}{d}\ \ <==>\ \ \varphi = \mu*id
$$
$$
\varphi(n) = \sum_{i=1}^{n}[\gcd(i, n)=1]
$$
$$
d(ij)=\sum_{x|i} \sum_{y|j}[\gcd(x, y)]
$$
$$
1 = \sum_{i|n}d(i)\mu(\frac{n}{i})\ \ <==>\ \ I=d*u
$$
$$
[n=1]=\sum_{d|n}\mu(d)\ \ <==>\ \ \xi=\mu*I
$$
$$
n = \sum_{i|n}\sigma(i)\mu(\frac{n}{i})\ \ <==>\ \ id=\sigma*\mu
$$
</code></pre>