82 lines
2.1 KiB
Plaintext
82 lines
2.1 KiB
Plaintext
{
|
|
"cells": [
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "1b6c514b",
|
|
"metadata": {},
|
|
"source": [
|
|
"# [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."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 1,
|
|
"id": "49b0126c",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"134043"
|
|
]
|
|
},
|
|
"execution_count": 1,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"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"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ebcdb94b",
|
|
"metadata": {},
|
|
"source": [
|
|
"## 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)."
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "SageMath 9.5",
|
|
"language": "sage",
|
|
"name": "sagemath"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
|
"version": "3.11.2"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|