Hi,

Normally, FactorInteger[] function outputs all the prime factors of a number as a list composed of the factors and their exponents, but I would like to see the output expressed as the sum of all the proper factors (all factors less than the value). Here are 3 examples that should help illustrate what I'm looking for:

1. FactorInteger[28] output would show {{2, 2}, {7, 1}} but I would like to see it expressed as:

    28 = 1 + 2 + 4 + 7 + 14
   

2. FactorInteger[496] outuput would show {{2, 4}, {31, 1}}, but I would like to see it expressed as:

   496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
   

3. FactorInteger[8128] output would show {{2,6}, {127, 1}}, but I would like to see it expressed as:

   8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064
   

I also just came across the Divisors[] function that creates a list of all possible divisors of a given value, which is sorta close, but would really like to see the values expressed as a sum rather than a list of values. I also found the Drop[] function that would remove the last element so that it's easy to see the entire list of proper divisors, but really would like to express it as a sum rather than the list. E.G.

In[1]:= Drop[Divisors[8128], -1]

Out[1]= {1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064}

So, how would I transform this to something like

8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064

Any suggestions?? Thanks very much...

-bob