quadratfrei | square-free

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

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).

binomial coefficient | biquadratefree | carefree couple | composite number | cubefree | Erdős squarefree conjecture | Feller-Tornier constant | Fibonacci number | Korselt's criterion | Möbius function | prime number | Riemann zeta function | Sárkőzy's theorem | squarefree factorization | squarefree part | squareful | square number | Sylvester's sequence

SquareFreeQ

college level