add problem 47

notebooks/problem0047.ipynb

@@ -0,0 +1,77 @@
+{
+ "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)"
+   ]
+  }
+ ],
+ "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
+}