{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Slow bruteforce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import functools\n",
    "import sympy\n",
    "\n",
    "\n",
    "@functools.lru_cache(maxsize=None)\n",
    "def aliquot_sum(n):\n",
    "    return sympy.divisor_sigma(n) - n\n",
    "\n",
    "\n",
    "def is_amicable(n):\n",
    "    return aliquot_sum(n) != n and aliquot_sum(aliquot_sum(n)) == n\n",
    "\n",
    "\n",
    "L = 10_000\n",
    "\n",
    "sum(n for n in range(2, L) if is_amicable(n))"
   ]
  }
 ],
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   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  },
  "title": "Amicable numbers"
 },
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