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  "body": "\n## Statement\n\nLet $f$ and $g$ be arithmetic functions, and let $n$ be a positive integer.\nThen\n$$(f * g)(n) = \\sum_{\\substack{a, b \\ge 1 \\\\ ab = n}} f(a) \\, g(b),$$\nwhere the sum runs over the ordered pairs of positive integers $(a, b)$ with $ab = n$, and $*$ is the [[Dirichlet convolution|0KH1N66QWW]].\n\n## Remarks\n\nThe map $d \\mapsto (d, n/d)$ is a bijection from the divisors of $n$ to these pairs. This gives the formula.\nThe symmetric form shows at once that $f * g = g * f$.\nFor example, $(f * g)(6) = f(1)g(6) + f(2)g(3) + f(3)g(2) + f(6)g(1)$.\n\n## Explanations\n\n### L1 human\n\nEach divisor $d$ of $n$ comes with its partner $n/d$.\nSo a sum over divisors is the same as a sum over the ways to write $n$ as an ordered product of two factors.\n",
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