Project Euler Q12 - LO Man Hei

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    "### Q12\n",
    "What is the value of the first triangle number to have over five hundred divisors?"
   ]
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    "def prod(x_vector):\n",
    "    result = 1\n",
    "    for i in x_vector:\n",
    "        result *= i\n",
    "    return result\n",
    "\n",
    "def list_count(x_vector):\n",
    "    result = {}\n",
    "    for x in x_vector:\n",
    "        result[x] = result.get(x,0) + 1\n",
    "    return result\n",
    "\n",
    "def prime_factors(n):\n",
    "    i = 2\n",
    "    factors = []\n",
    "    while i * i <= n:\n",
    "        if n % i:\n",
    "            i += 1\n",
    "        else:\n",
    "            n //= i\n",
    "            factors.append(i)\n",
    "    if n > 1:\n",
    "        factors.append(n)\n",
    "    return factors\n",
    "\n",
    "def num_divisors_of_triangle_num(n):\n",
    "    if n==1:\n",
    "        return 1\n",
    "    factors = prime_factors(n)\n",
    "    factors += prime_factors(n+1)\n",
    "    factors.remove(2)\n",
    "    return prod([i+1 for i in list_count(factors).values()])\n",
    "\n",
    "def triangle_num(n):\n",
    "    return (n+1)*n//2\n",
    "\n",
    "def triangle_num_with_over_n_num_divisors(n):\n",
    "    idx = 1\n",
    "    while True:\n",
    "        if num_divisors_of_triangle_num(idx) > n:\n",
    "            return triangle_num(idx)\n",
    "        idx += 1"
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      "CPU times: user 58.5 ms, sys: 0 ns, total: 58.5 ms\n",
      "Wall time: 55.5 ms\n"
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   "source": [
    "%%time\n",
    "triangle_num_with_over_n_num_divisors(500)"
   ]
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   "execution_count": null,
   "id": "64372508-1687-465e-b0ac-21c758dfd044",
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   "source": []
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