1

I am trying to generate a list of cubefree numbers (i.e. numbers when prime factorized contain no tripled factors) within a given range.

Of `DivisorSigma`

, `PrimeOmega`

, `Divisors`

, `PrimeNu`

and `FactorInteger`

, `FactorInteger`

seems to me to be the best suited to the task (please feel free to suggest more suitable methods). For example,

```
FactorInteger[630]
```

outputs

```
{{2, 1}, {3, 2}, {5, 1}, {7, 1}}
```

From this, I would like *Mathematica* to focus on the second number in each pair (the exponent) and determine which has the highest value. In this case, it is `{3,2}`

, indicating that `630`

is a cubefree number (i.e. - having no prime factor with a greater exponent than `2`

).

Is it possible to do this with a range of numbers, so that *Mathematica* evaluates each number in this way within a range, and then outputs that list of numbers?

many thanks for this. Is there any way to output a list of these - ie, to keep the numbers whose cubefree value is 'True' and delete thos from thelist that are 'False', and vice versa? – martin – 2013-11-19T11:44:44.403

1@martin see edit – Aky – 2013-11-19T11:47:24.133

@ Aky - fantastic! - thanks :) – martin – 2013-11-19T11:47:57.060