What is the correct name for a "summable" number?

Question

My math/CS teacher mentioned a function to me a few days ago (I don't remember the context), but didn't know the real name for it, so he just called it a summable function. We didn't really go into specifics much so I don't know how it works, but would like to. Not knowing the name is making Google searching very difficult, so I was hoping someone could recognise it and point me in the right direction.

The function does as follows: A number is considered "summable" if it is a positive integer, n, where all numbers from 1 to n can be made by a sum of any combination of the factors of n, where each factor is used only once. The function determines if the number is summable.

So for example, 12 is considered "summable" because each of the numbers from 1 through 12 can be made from some sum of the divisors 1, 2, 3, 4, 6, 12.

Using the above example, the numbers 1 through n are:

 1 = 1
 2 = 2
 3 = 3
 4 = 4
 5 = 1 + 4
 6 = 6
 7 = 1 + 6
 8 = 1 + 3 + 4
 9 = 1 + 2 + 6
10 = 4 + 6
11 = 1 + 4 + 6
12 = 12

As you can tell, there are other combinations of divisors that would equal the same number, like:

9 = 2 + 3 + 4

for instance.

Thanks!

Answer 1

It's called a practical number or sometimes panarithmic number.