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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "22f94a3b",
+   "metadata": {},
+   "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."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "6747d2a3",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "4179871\n"
+     ]
+    }
+   ],
+   "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",
+    "        if n - m in abundant_numbers:\n",
+    "            non_abundant_sums.discard(n)\n",
+    "            break\n",
+    "\n",
+    "print(sum(non_abundant_sums))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "91a43bd1",
+   "metadata": {},
+   "source": [
+    "## Relevant sequences\n",
+    "* Numbers that are not the sum of two abundant numbers: [A048242](https://oeis.org/A048242)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}