# multiplicative functions for factored integers

Since integer factorization is rather expensive computationally, its result sometimes represent quite a valuable piece of information that we do not want to recompute. Sage provides `Factorization`

object for dealing factored integer (and more generally rational) numbers, and even supports multiplication / division of such integers - like `factor(1000) / factor(10)`

.

However, while it is easy to compute multiplicative functions for a given `Factorization`

object, such standard multiplicative functions as `number_of_divisors()`

, `sigma()`

, `divisors()`

, etc. are missing for `Factorization`

objects. Also, `factor()`

function should also trivially work for them, returning just the given `Factorization`

object (currently we get a weird error like `TypeError: unable to factor 2 * 5`

).

Do I miss something here?