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  "body": "\n## Definition\n\nAn [[arithmetic function|0H2EPRZC0D]] $f$ is multiplicative if $f(1) = 1$ and $f(mn) = f(m) f(n)$ for all [[coprime|0GFKP8F8AG]] positive integers $m$ and $n$.\n\n## Remarks\n\nA multiplicative function is determined by its values at prime powers: if $n = p_1^{e_1} \\cdots p_k^{e_k}$, then $f(n) = f(p_1^{e_1}) \\cdots f(p_k^{e_k})$.\nExamples are [[Euler's totient function|0VV04M41AN]], the [[divisor function|0YEW47VJ0J]] and the [[Möbius function|0C8QENHYZW]].\nA function with $f(mn) = f(m) f(n)$ for all $m$ and $n$ is [[completely multiplicative|0GS27TKF1V]].\n\n## Explanations\n\n### L1 human\n\nFor a multiplicative function, you can compute $f(n)$ from the prime factorization of $n$.\nFor example, $\\varphi(12) = \\varphi(4) \\varphi(3) = 2 \\cdot 2 = 4$, because $4$ and $3$ are coprime.\n",
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