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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(), seem to missing for Factorization objects. Also, factor function should also trivially work for them, returning just the given Factorization object.

Do I miss something here?

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(), seem to missing for Factorization objects. Also, factorfactor() function should also trivially work for them, returning just the given Factorization object.

Do I miss something here?

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(), seem to missing for Factorization objects. Also, factor() function should also trivially work for them, returning just the given Factorization object.object (currently get a weird error like TypeError: unable to factor 2 * 5).

Do I miss something here?

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. seem to 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?

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. seem to be 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?

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. seem to be 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?