Questions tagged [square-free]

An element of an integral domain is called *square-free* if it isn’t divisible by any non-unit square. Most notable applications are square-free integers and square-free polynomials.

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36 votes
3 answers
5k views

$\prod_{n=1}^{\infty} n^{\mu(n)}=\frac{1}{4 \pi ^2}$

When I tested this in Mathematica, I had expected it to say it did not converge. However, I got this: $$\prod_{n=1}^\infty n^{\mu(n)}=\frac{1}{4 \pi ^2}$$ Note: this is the reciprocal of (3) zeta-...
Fred Daniel Kline's user avatar
18 votes
4 answers
3k views

are there infinitely many triples of consecutive square-free integers?

The title says it all ... Obviously, any such triple must be of the form $(4a+1,4a+2,4a+3)$ where $a$ is an integer. Has this problem already been studied before ? The result would follow from Dickson'...
Ewan Delanoy's user avatar
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