Notation for an integer being square-free

Question

An integer $n \neq 0$ is square-free if $n$ is divisible by no prime square. Can you figure out any notation for simplifying this long description?

It may be guessed that $p^{2} \nmid n$ for any prime $p$ is okay, but this is still a bit long.

There is no standard notation. As for characterizations, besides $,a^2\mid n,\Rightarrow, a\mid 1,,$ there are many others. — Bill Dubuque, Aug 28 '14 at 04:06

André Nicolas · Accepted Answer · 2014-08-28T04:19:01.093

2

Well, we could use $\mu(n)\ne 0$. Here $\mu$ is the Möbius function. I prefer (by a lot) to say square-free.

edited Aug 28 '14 at 04:19

answered Aug 28 '14 at 04:05

André Nicolas

Ah right! It is the Mobius function that I cannot recall. – Yes Aug 28 '14 at 04:10
Should be $,\mu(n)\color{#c00}\neq 0\ \ $ – Bill Dubuque Aug 28 '14 at 04:18
@BillDubuque: Thanks for catching it. This may be a personal record for error to length ratio. – André Nicolas Aug 28 '14 at 04:20

Coward · Answer 2 · 2019-04-29T00:03:36.787

1

$n=ab$ implies $gcd(a,b)=1$ for all $a,b$.

edited Apr 29 '19 at 00:03

answered Aug 28 '14 at 04:03

Coward

2 Answers2