Question 491972
<pre>
For any integer the numbers

A. one of its factors 

and 

B. {{{(that_integer)/(that_factor)}}} 

are two different integers except when the integer is a
perfect square and that factor is its square root.

So only perfect squares have an odd number of factors, since
its square root and {{{(that_perfect_square)/(its_square_root)}}} are not two different
factors, but only one factor, since those are the same number. 

So it has to be a perfect square to have 5 factors.
So it has to be one of these:

16, 25, 36, 49, 64, or 81

16 is not divisible by 1+6, which is 7

25 is not divisible by 2+5, which is 7

36 IS divisible by 3+6, which is 9.  However 36 has 
       9 factors 1,2,3,4,6,9,12,18, and 36, and that's too many.

64 is not divisible by 6+4, which is 10.

81 is divisible by 8+1, which is 9.  It's factors are 1,3,9,27, and 81.
       And that's 5, so the number is 81.

Answer: The sum of the factors is 1+3+9+27+81 = 121

Edwin</pre>