SquareFreeQ[expr] gives True if expr is a square-free polynomial or number, and False otherwise.
SquareFreeQ[expr, vars]gives True if expr is square free with respect to the variables vars.
12 has a factor 4, which is a square:
FactorInteger Factor FactorSquareFree PolynomialGCD IrreduciblePolynomialQ Discriminant PrimeQ PrimePowerQ MoebiusMu
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