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    "# [Non-Abundant Sums](https://projecteuler.net/problem=23)\n",
    "\n",
    "Just like in [problem 21](https://projecteuler.net/problem=21), we'll define an `aliquot_sum` function and use that to find all the [abundant numbers](https://en.wikipedia.org/wiki/Abundant_number) below 28,124 (as in problem 21, we could instead use a sieve to compute the divisor sums)."
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    "aliquot_sum = lambda n: sigma(n) - n\n",
    "abundant_numbers = {k for k in range(1, 28124) if aliquot_sum(k) > k}"
   ]
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   "source": [
    "Then we check every integer less than 28,124 to see if it's the sum of any two abundant numbers, and if it is, remove it from a set containing all those integers. Whatever's left in that set are the non-abundant sums."
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    "non_abundant_sums = set(range(1, 28124))\n",
    "for n in range(1, 28124):\n",
    "    for m in abundant_numbers:\n",
    "        if n - m in abundant_numbers:\n",
    "            non_abundant_sums.discard(n)\n",
    "            break\n",
    "\n",
    "sum(non_abundant_sums)"
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   "source": [
    "## Relevant sequences\n",
    "* Sums of divisors: [A000203](https://oeis.org/A000203)\n",
    "* Numbers that are not the sum of two abundant numbers: [A048242](https://oeis.org/A048242)\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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