@Eryndis Let me know if you make any progress with those hints or with the exercise about tau(n) being odd.

@Eryndis Well, tell me what exactly you want. Was I correct in guessing that for each i you want the smallest positive n such that tau(n) = i (a partial inverse of tau)? Would any positive n, not necessarily the smallest, such that tau(n) = i be good enough?

My hint about that line of code was not that you would use it in a program, but that you would use it to understand how tau is computed. Once you know how tau is computed, it should be relatively easy to figure out how to write code for a partial inverse that runs in a short amount of time.

Hint 2: For a bunch of different numbers n, look at ifactors(n) and ifactors(tau(n)). What is the pattern?

Here is a related, but simpler, exercise: What are necessary and sufficient conditions for tau(n) to be odd? This one is a standard in mathematical puzzle collections for the general public, although it is always stated in more fanciful form referring to a long hallway of numbered locker doors or pull-chain lights. See http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.51262.html

@Eryndis Well, tell me what exactly you want. Was I correct in guessing that for each i you want the smallest positive n such that tau(n) = i (a partial inverse of tau)? Would any positive n, not necessarily the smallest, such that tau(n) = i be good enough?

My hint about that line of code was not that you would use it in a program, but that you would use it to understand how tau is computed. Once you know how tau is computed, it should be relatively easy to figure out how to write code for a partial inverse that runs in a short amount of time.

Hint 2: For a bunch of different numbers n, look at ifactors(n) and ifactors(tau(n)). What is the pattern?

Here is a related, but simpler, exercise: What are necessary and sufficient conditions for tau(n) to be odd? This one is a standard in mathematical puzzle collections for the general public, although it is always stated in more fanciful form referring to a long hallway of numbered locker doors or pull-chain lights. See http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.51262.html

Please upload an example.

Do you want to expand for an arbitrary unknown positive integer n, or specific values of n? 

In order for me to take this product seriously, you'll need to correct the spelling and grammar on the web page that your post linked to (the Maple IDE page, not the YouTube video). I found 11 errors on the first screen alone. I am not used to seeing this shoddiness in MapleSoft promotional materials. If MapleSoft associates themselves with this product, it will damage their reputation.

Does the Maple 16 itself (the final installed application as opposed to the installer) need to be run in the compatibility mode? or is it that only the installer needs to run in compatibility mode and the Maple 16, once installed, can run in full regular Windows 8 (64-bit)?

Does the Maple 16 itself (the final installed application as opposed to the installer) need to be run in the compatibility mode? or is it that only the installer needs to run in compatibility mode and the Maple 16, once installed, can run in full regular Windows 8 (64-bit)?

> Multiple assignment to a vector causes different names pointing to the same object.

It is not multiple assignment that causes the problem.  The problem is that the left-side argument to $ is evaluated before being duplicated, as are most operands to most operators.  So both of the following will work, producing two distinct vectors:

v1, v2:= 'Vector'(2) $ 2;

or

v1,v2:= seq(Vector(2), k= 1..2);

> Multiple assignment to a vector causes different names pointing to the same object.

It is not multiple assignment that causes the problem.  The problem is that the left-side argument to $ is evaluated before being duplicated, as are most operands to most operators.  So both of the following will work, producing two distinct vectors:

v1, v2:= 'Vector'(2) $ 2;

or

v1,v2:= seq(Vector(2), k= 1..2);