diff --git a/notebooks/problem0021.ipynb b/notebooks/problem0021.ipynb
index d0469c9..210dd39 100644
--- a/notebooks/problem0021.ipynb
+++ b/notebooks/problem0021.ipynb
@@ -132,6 +132,22 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "def update_multiples(dsum, p, limit):\n",
+    "    q = p\n",
+    "    while True:\n",
+    "        # sigma(a*b) = sigma(a) * sigma(b) if gcd(a, b) = 1\n",
+    "        for k in range(2 * q, limit, q):\n",
+    "            if k % (p*q) != 0:\n",
+    "                dsum[k] *= dsum[q]\n",
+    "\n",
+    "        if p * q >= limit:\n",
+    "            break\n",
+    "\n",
+    "        # sigma(p^k) = p^k + sigma(p^(k-1))\n",
+    "        dsum[p*q] = p * q + dsum[q]\n",
+    "        q *= p\n",
+    "        \n",
+    "\n",
     "def sum_of_divisors_range(limit):       \n",
     "    dsum = [1 for n in range(0, limit)]\n",
     "    dsum[0] = 0\n",
@@ -144,21 +160,7 @@
     "\n",
     "        # n is prime\n",
     "        dsum[n] = n + 1\n",
-    "\n",
-    "        m = n\n",
-    "        while True:\n",
-    "            # sigma(a*b) = sigma(a) * sigma(b) if gcd(a, b) = 1\n",
-    "            for k in range(2 * m, limit, m):\n",
-    "                if k % (m*n) != 0:\n",
-    "                    dsum[k] *= dsum[m]\n",
-    "\n",
-    "            if m * n >= limit:\n",
-    "                break\n",
-    "                \n",
-    "            # sigma(p^k) = p^k + sigma(p^(k-1))\n",
-    "            dsum[m*n] = m*n + dsum[m]\n",
-    "            m *= n\n",
-    "            \n",
+    "        update_multiples(dsum, n, limit)\n",
     "        yield dsum[n]"
    ]
   },