Correct function count_divisors

C/projecteuler.c

@@ -143,7 +143,7 @@ int *sieve(int n)
     * there is no need check i>sqrt(n).*/
    limit = floor(sqrt(n));
 
-   for(i = 3; i < limit; i += 2)
+   for(i = 3; i <= limit; i += 2)
    {
       /* Find the next number not crossed out, which is prime.*/
       if(primes[i])
@@ -166,19 +166,23 @@ int count_divisors(int n)
 {
    int i, limit, count = 0;
 
+   /* For every divisor below the square root of n, there is a corresponding one
+    * above the square root, so it's sufficient to check up to the square root of n
+    * and count every divisor twice. If n is a perfect square, the last divisor is
+    * wrongly counted twice and must be corrected.*/ 
    limit = floor(sqrt(n));
 
-   for(i = 1; i < limit; i++)
+   for(i = 1; i <= limit; i++)
    {
       if(n % i == 0)
       {
          count += 2;
       }
-
-      if(n == limit * limit)
-      {
-         count--;
-      }
+   }
+   
+   if(n == limit * limit)
+   {
+      count--;
    }
 
    return count;

Python/projecteuler.py

@@ -19,6 +19,21 @@ def is_prime(num):
 
     return True
 
+def is_palindrome(num, base):
+    reverse = 0
+
+    tmp = num
+
+    while tmp > 0:
+        reverse = reverse * base
+        reverse = reverse + tmp % base
+        tmp = tmp // base
+
+    if num == reverse:
+        return True
+
+    return False
+
 def lcm(a, b):
     return a * b // gcd(a, b)
 
@@ -60,26 +75,11 @@ def count_divisors(n):
         if n % i == 0:
             count = count + 2
 
-        if n == limit * limit:
-            count = count - 1
+    if n == limit * limit:
+        count = count - 1
 
     return count
 
-def is_palindrome(num, base):
-    reverse = 0
-
-    tmp = num
-
-    while tmp > 0:
-        reverse = reverse * base
-        reverse = reverse + tmp % base
-        tmp = tmp // base
-
-    if num == reverse:
-        return True
-
-    return False
-
 def is_pandigital(value, n):
     i = 0
     digits = zeros(n + 1, int)