minor edits

notebooks/problem0023.ipynb

@@ -7,28 +7,46 @@
    "source": [
     "# [Non-Abundant Sums](https://projecteuler.net/problem=23)\n",
     "\n",
-    "Just like in [problem 21](https://projecteuler.net/problem=21), we'll define an `aliquot_sum` function and use that to find all the [abundant numbers](https://en.wikipedia.org/wiki/Abundant_number) below 28,124. Then we check every integer less than 28,124 to see if it's the sum of any two abundant numbers, and if it is, remove it from a set containing all those integers. Whatever's left in that set are the non-abundant sums."
+    "Just like in [problem 21](https://projecteuler.net/problem=21), we'll define an `aliquot_sum` function and use that to find all the [abundant numbers](https://en.wikipedia.org/wiki/Abundant_number) below 28,124 (as in problem 21, we could instead use a sieve to compute the divisor sums)."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 1,
+   "id": "84f3ad0c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "aliquot_sum = lambda n: sigma(n) - n\n",
+    "abundant_numbers = {k for k in range(1, 28124) if aliquot_sum(k) > k}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d6586d17",
+   "metadata": {},
+   "source": [
+    "Then we check every integer less than 28,124 to see if it's the sum of any two abundant numbers, and if it is, remove it from a set containing all those integers. Whatever's left in that set are the non-abundant sums."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
    "id": "6747d2a3",
    "metadata": {},
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "4179871\n"
-     ]
+     "data": {
+      "text/plain": [
+       "4179871"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "aliquot_sum = lambda n: sigma(n) - n\n",
-    "\n",
-    "abundant_numbers = {k for k in range(1, 28124) if aliquot_sum(k) > k}\n",
-    "\n",
     "non_abundant_sums = set(range(1, 28124))\n",
     "for n in range(1, 28124):\n",
     "    for m in abundant_numbers:\n",
@@ -36,7 +54,7 @@
     "            non_abundant_sums.discard(n)\n",
     "            break\n",
     "\n",
-    "print(sum(non_abundant_sums))"
+    "sum(non_abundant_sums)"
    ]
   },
   {