Mathematical notation

Question

Is there some generally accepted notation for squarefree, cubefree, etc. numbers?

And is there also some notation for squareful, cubeful, etc. numbers?

BIS HD · Accepted Answer · 2013-12-06T10:59:47.143

2

I don't think there is any generally accepted notation for those numbers. But you could of course define those sets, for example the cubefree numbers

$$\Bbb Z_{c.f.} = \{a \in \Bbb Z \mid \not\exists b \in \Bbb Z \setminus \{1,-1\} \text{ s.t. } b^3 \mid a \}$$

or else.

edited Dec 06 '13 at 10:59

answered Dec 05 '13 at 15:15

BIS HD

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Great - thanks for the reply. – martin Dec 05 '13 at 15:44
Could you say $$\Bbb Z_{c.f.} = {a \in \Bbb Z \mid \not\exists a^3 \in \Bbb Z }$$? – martin Dec 05 '13 at 16:07
... Is the $\text{s.t.}$ necessary? – martin Dec 05 '13 at 16:13
... What do you mean by $\text{s.t.}$? – martin Dec 05 '13 at 16:14
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This definition isn't right, I don't think (or one of us is misunderstanding "cubefree"). You've defined the set of integers that aren't cubes, not the set of integers that have no cubes as divisors. – mjqxxxx Dec 05 '13 at 16:55
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@mjqxxxx You are, of course, right! S.t. means such that – BIS HD Dec 06 '13 at 10:59
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You need $b\ne1$. – lhf Dec 06 '13 at 11:00
@lhf yes, thank you. and $b \neq -1$ as well. – BIS HD Dec 06 '13 at 11:02

Mathematical notation

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