find total number of divisors of number, for t test cases in python

Question

i make a programe to find the number of divisor for a number with test case to submit it on the online judge so i write the code like that

num_case=int(raw_input())
num=list()
final_o=[]
for x in xrange(num_case):
     num.append(int(raw_input()))
for h in num:
     result=[int(h)]
for i in xrange(1, h + 1):
    if h % i == 0:
        result.append(i)
a=final_o.append(len(result)-1)
for ff in final_o:
     print ff

in this case i make user input the number of test case for example 3 and then enter the number for example 12 7 and 36 then he get the output like this 6 2 9 that the 12 have 6 divisor number and so on this code work well but i get Memory Error when i submit it so i try to use itertools because range in for loop is small and xrange take a lot of time more than 2 second but i dont get any output code

from itertools import count
num_case=int(raw_input())
num=list()
final_o=[]
for x in xrange(num_case):
     num.append(int(raw_input()))
for h in num:
    result=[int(h)]
    n=int(raw_input())
for i in count(1):
    if n % i == 0:
        result.append(i)
    elif count==n+1:
        break
a=final_o.append(len(result)-1)
for ff in final_o:
   print ff

any one have a solution to this bug ? Note that the time for the test case 2 second and the range of the numbers is 10^9 and test case 100 How i Do that ?

Answer 1

def devisors_number(n):
    result = 0
    sqrt_n = int(n**0.5)

    for i in xrange(1, sqrt_n + 1):
        if n % i == 0:
            result += 1

    result *= 2

    if sqrt_n**2 == n:
        result -= 1

    return result


n = int(raw_input("Enter a number: "))
d = devisors_number(n)
print "{0} has {1} devisors".format(n, d)