Jordan-Pólya numbers: Difference between revisions
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The 3,800th Jordan-Pólya number is : 7,213,895,789,838,336
= (4!)⁸ x (2!)¹⁶
</pre>
=={{header|C#}}==
{{trans|Java}}
<syntaxhighlight lang="C#">
using System;
using System.Collections.Generic;
using System.Linq;
public class JordanPolyaNumbers
{
private static SortedSet<long> jordanPolyaSet = new SortedSet<long>();
private static Dictionary<long, SortedDictionary<int, int>> decompositions = new Dictionary<long, SortedDictionary<int, int>>();
public static void Main(string[] args)
{
CreateJordanPolya();
long belowHundredMillion = jordanPolyaSet.LastOrDefault(x => x < 100_000_000L);
List<long> jordanPolya = new List<long>(jordanPolyaSet);
Console.WriteLine("The first 50 Jordan-Polya numbers:");
for (int i = 0; i < 50; i++)
{
Console.Write($"{jordanPolya[i],5}{(i % 10 == 9 ? "\n" : "")}");
}
Console.WriteLine();
Console.WriteLine("The largest Jordan-Polya number less than 100 million: " + belowHundredMillion);
Console.WriteLine();
foreach (int i in new List<int> { 800, 1050, 1800, 2800, 3800 })
{
Console.WriteLine($"The {i}th Jordan-Polya number is: {jordanPolya[i - 1]} = {ToString(decompositions[jordanPolya[i - 1]])}");
}
}
private static void CreateJordanPolya()
{
jordanPolyaSet.Add(1L);
SortedSet<long> nextSet = new SortedSet<long>();
decompositions[1L] = new SortedDictionary<int, int>();
long factorial = 1;
for (int multiplier = 2; multiplier <= 20; multiplier++)
{
factorial *= multiplier;
foreach (long number in new SortedSet<long>(jordanPolyaSet))
{
long newNumber = number;
while (newNumber <= long.MaxValue / factorial)
{
long original = newNumber;
newNumber *= factorial;
nextSet.Add(newNumber);
decompositions[newNumber] = new SortedDictionary<int, int>(decompositions[original]);
if (decompositions[newNumber].ContainsKey(multiplier))
{
decompositions[newNumber][multiplier]++;
}
else
{
decompositions[newNumber][multiplier] = 1;
}
}
}
jordanPolyaSet.UnionWith(nextSet);
nextSet.Clear();
}
}
private static string ToString(SortedDictionary<int, int> map)
{
string result = "";
foreach (int key in map.Keys)
{
result = key + "!" + (map[key] == 1 ? "" : "^" + map[key]) + " * " + result;
}
return result.TrimEnd(' ', '*');
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 50 Jordan-Polya numbers:
1 2 4 6 8 12 16 24 32 36
48 64 72 96 120 128 144 192 216 240
256 288 384 432 480 512 576 720 768 864
960 1024 1152 1296 1440 1536 1728 1920 2048 2304
2592 2880 3072 3456 3840 4096 4320 4608 5040 5184
The largest Jordan-Polya number less than 100 million: 99532800
The 800th Jordan-Polya number is: 18345885696 = 4!^7 * 2!^2
The 1050th Jordan-Polya number is: 139345920000 = 8! * 5!^3 * 2!
The 1800th Jordan-Polya number is: 9784472371200 = 6!^2 * 4!^2 * 2!^15
The 2800th Jordan-Polya number is: 439378587648000 = 14! * 7!
The 3800th Jordan-Polya number is: 7213895789838336 = 4!^8 * 2!^16
</pre>
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