Sum of divisors

Sum of divisors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Given a positive integer, sum its positive divisors.

Task

Show the result for the first 100 positive integers.

Python

<lang Python> def factorize(n):

   assert(isinstance(n, int))
   if n < 0: 
       n = -n 
   if n < 2: 
       return 
   k = 0 
   while 0 == n%2: 
       k += 1 
       n //= 2 
   if 0 < k: 
       yield (2,k) 
   p = 3 
   while p*p <= n: 
       k = 0 
       while 0 == n%p: 
           k += 1 
           n //= p 
       if 0 < k: 
           yield (p,k)
       p += 2 
   if 1 < n: 
       yield (n,1) 

def sum_of_divisors(n):

   assert(n != 0) 
   ans = 1 
   for (p,k) in factorize(n): 
       ans *= (pow(p,k+1) - 1)//(p-1) 
   return ans 
   

if __name__ == "__main__":

   print([sum_of_divisors(n) for n in range(1,101)])</lang>

Output:

[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 57, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144, 68, 126, 96, 144, 72, 195, 74, 114, 124, 140, 96, 168, 80, 186, 121, 126, 84, 224, 108, 132, 120, 180, 90, 234, 112, 168, 128, 144, 120, 252, 98, 171, 156, 217]