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    Square-free

    Alternate names
    Basic definition

    A positive integer is squarefree if it is not divisible by any perfect square greater than one.

    Detailed definition

    A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially squarefree. The number 1 is by convention taken to be squarefree. The squarefree numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, ... (OEIS A005117). The squareful numbers (i.e., those that contain at least one square) are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (OEIS A013929).

    Related Wolfram Language symbol

    SquareFreeQ

    Educational grade level

    college level

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