Editing Square-free integer (section)

{{Short description|Number without repeated prime factors}}
[[File:Composite number Cuisenaire rods 10.svg|thumb|10 is square-free, as its divisors greater than 1 are 2, 5, and 10, none of which is square (the first few squares being 1, 4, 9, and 16)]]
[[File:squarefree_numbers_sieve.svg|thumb|Square-free integers up to 120 remain after eliminating multiples of squares of primes up to √120]]
In [[mathematics]], a '''square-free integer''' (or '''squarefree integer''') is an [[integer]] which is [[divisor|divisible]] by no [[square number]] other than 1. That is, its [[prime factorization]] has exactly one factor for each prime that appears in it. For example, {{nowrap|1=10 = 2 ⋅ 5}} is square-free, but {{nowrap|1=18 = 2 ⋅ 3 ⋅ 3}} is not, because 18 is divisible by {{nowrap|1=9 = 3<sup>2</sup>}}. The smallest positive square-free numbers are
{{bi|left=1.6|1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, ... {{OEIS|id=A005117}}}}