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  "body": "\n## Definition\n\nA nonzero integer $n$ is square-free when no square of a [[prime number|0SN0MAEKYX]] divides $n$.\nThat is, there is no prime $p$ such that $p^2 \\mid n$.\n\n## Remarks\n\nEquivalently, $n$ is square-free when the only perfect squares that divide $n$ are $1$.\nA positive integer is square-free if and only if each exponent in its [[prime factorization|0AEKDFCYFA]] is $1$.\nThe first square-free positive integers are $1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15$. The integer $12 = 2^2 \\cdot 3$ is not square-free.\nThe integer $0$ is not square-free, because each square divides $0$.\n\n## Explanations\n\n### L1 human\n\nA number is square-free when no prime appears twice in its factorization.\nFor example, $30 = 2 \\cdot 3 \\cdot 5$ is square-free, but $18 = 2 \\cdot 3 \\cdot 3$ is not, because $9$ divides $18$.\n",
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