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- A square-free number is a number that is not divisible by the square of any positive integer123. Examples of square-free numbers include412:
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Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.A number is said to be square-free if no prime factor divides it more than once, i.e., the largest power of a prime factor that divides n is one. First few square-free numbers are 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, …www.geeksforgeeks.org/square-free-number/For example, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 32. The smallest positive square-free numbers are 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,... (sequence A005117 in the OEIS)en.wikipedia.org/wiki/Square-free_integerSquarefree: If a number is not divisible by the square of any positive integer, it is squarefree. For example, 21 = 3 ⋅ 7 21 = 3 ⋅ 7 is a squarefree number and 20 =22 ⋅ 5 20 = 2 2 ⋅ 5 is not.math.stackexchange.com/questions/73535/proof-re…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).mathworld.wolfram.com/Squarefree.html - People also ask
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In mathematics, a square-free integer (or squarefree integer) is an integer which is 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, 10 = 2 ⋅ 5 is square-free, but 18 = 2 ⋅ 3 ⋅ 3 is not, because 18 is divisible by 9 = 3 . The … See more
The radical of an integer is its largest square-free factor, that is $${\displaystyle \textstyle \prod _{i=1}^{k}q_{i}}$$ with notation of the preceding section. An integer is square-free See more
The absolute value of the Möbius function is the indicator function for the square-free integers – that is, |ÎĽ(n)| is equal to 1 if n is square-free, and 0 if … See more
If we represent a square-free number as the infinite product
then we may take … See moreLet us call "t-free" a positive integer that has no t-th power in its divisors. In particular, the 2-free integers are the square-free integers. See more
A positive integer $${\displaystyle n}$$ is square-free if and only if in the prime factorization of $${\displaystyle n}$$, no prime factor occurs … See more
The central binomial coefficient
$${\displaystyle {2n \choose n}}$$
is never squarefree for n > 4. This was proven in 1985 for all sufficiently large integers by See moreWikipedia text under CC-BY-SA license WEB6 days ago · 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 …
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