eulerbooks/notebooks/problem0047.ipynb

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    "# [Distinct Primes Factors](https://projecteuler.net/problem=47)\n",
    "\n",
    "The [prime omega function](https://en.wikipedia.org/wiki/Prime_omega_function) $\\omega(n)$ counts the number of distinct prime factors of $n$. SageMath provides this function through the [PARI/GP interface](https://doc.sagemath.org/html/en/reference/interfaces/sage/interfaces/gp.html), but we can also just look at the length of the output of the built-in `factor` function.\n",
    "\n",
    "See [problem 3](https://projecteuler.net/problem=3) for information on implementing a factorization function."
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    "from itertools import count\n",
    "\n",
    "def omega(n):\n",
    "    return len(factor(n))\n",
    "\n",
    "\n",
    "for n in count(1):\n",
    "    if all(omega(n+k) == 4 for k in (0,1,2,3)):\n",
    "        break\n",
    "\n",
    "n"
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    "## Relevant sequences\n",
    "* Number of distinct prime factors: [A001221](https://oeis.org/A001221)\n",
    "\n",
    "#### Copyright (C) 2025 filifa\n",
    "\n",
    "This work is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International license](https://creativecommons.org/licenses/by-sa/4.0/) and the [BSD Zero Clause license](https://spdx.org/licenses/0BSD.html)."
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