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  • https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/An_Introduction_to_Number_Theory_(Veerman)/04%3A_Number_Theoretic_Functions/4.04%3A_New_Page
    From the definition of Euler’s phi function, we see that the cardinality |S(d,n)| of S(d,n) is given by φ(nd). \[n = \sum_{d|n} |S(d,n)| = \sum_{d|n} \varphi(\frac{d}{n}) \...From the definition of Euler’s phi function, we see that the cardinality |S(d,n)| of S(d,n) is given by φ(nd). n=d|n|S(d,n)|=d|nφ(dn) φ(n)=d|nμ(d)nd=nd|nμ(d)d φ(ri=1plii=ri=1φ(plii) φ(pl)=pllj=0μ(pj)pj=pl(11p)

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