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  "body": "\n## Definition\n\nAn arithmetic function is a function $f \\colon \\mathbb{Z}_{\u003e0} \\to \\mathbb{C}$ from the positive integers to the complex numbers.\n\n## Remarks\n\nExamples are [[Euler's totient function|0VV04M41AN]] $\\varphi$, the [[divisor function|0YEW47VJ0J]] $\\sigma_k$ and the [[Möbius function|0C8QENHYZW]] $\\mu$.\nSome texts allow values in another commutative ring, or set $f(0) = 0$ and use all natural numbers as the domain.\nThe [[Dirichlet convolution|0KH1N66QWW]] makes the arithmetic functions into a commutative ring.\n\n## Explanations\n\n### L1 human\n\nAn arithmetic function is a sequence $f(1), f(2), f(3), \\dots$ of numbers, seen as a function of $n$.\nNumber theory studies such functions when they describe arithmetic properties of $n$, such as its number of divisors.\n",
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