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Building on this question, if the cubeful numbers were defined as follows:

$$\Bbb Z_{\{3+\}} = \{a \in \Bbb Z \mid \not\exists b \in \Bbb Z \text{ s.t. } a \neq b^3 \}$$

Would it suffice to say that: $$\text{ If }\ \Bbb Z_{\{3+\}} = \{a \in \Bbb Z \mid \not\exists b \in \Bbb Z \text{ s.t. } a \neq b^3 \}$$ $$\text{ then }\ n_{\{3+\}3}=18$$

for example? Is the $\text{ s.t. }$ necessary?

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martin
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    The set you defined contains those integers that are equal to the cube of every integer; i.e., it's the empty set. What do you mean to say? Does "cubeful" mean divisible by a cube? – mjqxxxx Dec 05 '13 at 16:53
  • Yes, I do mean divisible by a cube! - Doesn't 'divisible by' have the same symbol as 'such that' ...? – martin Dec 05 '13 at 17:25

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