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# Completely multiplicative sequences

${\displaystyle \forall \,m,\,n\,\in \,\mathbb {N} ,\,a(mn)\,=\,a(m)\,a(n).\,}$
Since ${\displaystyle \scriptstyle a(n)\,=\,a(1n)\,=\,a(1)\,a(n)\,}$, we then have ${\displaystyle \scriptstyle a(1)\,=\,1.\,}$