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  "body": "\n## Definition\n\nLet $k$ be a natural number.\nThe divisor function $\\sigma_k$ is the [[arithmetic function|0H2EPRZC0D]] given by\n$$\\sigma_k(n) = \\sum_{d \\mid n} d^k,$$\nwhere the sum runs over the [[positive divisors|0FCWA16FZE]] $d$ of $n$.\n\n## Remarks\n\nThe case $k = 0$ is the [[number of divisors|0BKJT6WG96]], and the case $k = 1$ is the [[sum of divisors|009QCP5T3Z]].\nFor example, $\\sigma_2(6) = 1 + 4 + 9 + 36 = 50$.\nThe same formula defines $\\sigma_k$ for each real or complex number $k$.\nThe function $\\sigma_k$ is [[multiplicative|04WC36XKV6]].\n\n## Explanations\n\n### L1 human\n\nTo compute $\\sigma_k(n)$, list the divisors of $n$, raise each one to the power $k$, and add the results.\n",
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