{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools, sympy\n",
    "\n",
    "def aliquot_sum(n):\n",
    "    return sympy.divisor_sigma(n) - n\n",
    "\n",
    "abundants = {n for n in range(2, 28123 + 1) if aliquot_sum(n) > n}\n",
    "sum_of_abundants = set(a + b for (a, b) in itertools.combinations_with_replacement(abundants, 2))\n",
    "sum(set(range(1, 28123+1)) - sum_of_abundants)"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "title": "Non-abundant sums"
 },
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}