Euler 063 - Powerful digit counts.ipynb

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    "Euler Problem 63\n",
    "================\n",
    "\n",
    "The 5-digit number, 16807=7<sup>5</sup>, is also a fifth power. Similarly, the 9-digit number, 134217728=8<sup>9</sup>, is a ninth power.\n",
    "\n",
    "How many n-digit positive integers exist which are also an nth power?\n"
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      "49\n"
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    "print (9 + sum(9 - int(10**(1-1.0/n)) for n in range(2, 22)))"
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   "source": [
    "**Explanation:** The one-digit numbers from 1 to 9 are first powers. Assume that $n \\ge 2$.\n",
    "\n",
    "We wish to count the solutions to $10^{n-1} \\le k^n < 10^n$ where $k, n \\ge 2$.\n",
    "This equation is equivalent to $10^{1-1/n} \\le k \\le 9$."
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