Euler 124 - Ordered radicals.ipynb

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    "Euler Problem 124\n",
    "=================\n",
    "\n",
    "The radical of n, rad(n), is the product of distinct prime factors of n. For\n",
    "example, 504 = 23 × 32 × 7, so rad(504) = 2 × 3 × 7 = 42.\n",
    "\n",
    "If we calculate rad(n) for 1 ≤ n ≤ 10, then sort them on rad(n), and sorting\n",
    "on n if the radical values are equal, we get:\n",
    "\n",
    "\n",
    "Let E(k) be the kth element in the sorted n column; for example, E(4) = 8 and\n",
    "E(6) = 9.\n",
    "\n",
    "If rad(n) is sorted for 1 ≤ n ≤ 100000, find E(10000).\n",
    "\n",
    "\n",
    "        \n",
    "        \n",
    "        "
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    "N = 100000\n",
    "K = 10000\n",
    "rad = [1]*(N+1)\n",
    "for p in range(2, N+1):\n",
    "    if rad[p] == 1:\n",
    "        for k in range(p, N+1, p):\n",
    "            rad[k] *= p\n",
    "\n",
    "print(sorted([[rad[n],n] for n in range(1,N+1)])[K-1][1])"
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