Pycharm 2016.3.2 community edition

Their licensing is a bit complicated.
They seem to use a new licensing model. You can get a time limited license, if your project complies to their requirements.
https://www.jetbrains.com/buy/opensource/?product=pycharm
The latest license version is found here:
https://www.jetbrains.com/store/license_opensource.html

It's not the same as on their GitHub:
https://github.com/JetBrains/intellij-community

Their different licensing shemes can be found here:
https://www.jetbrains.com/store/terms/comparison.html#LicenseComparison

I did not dig too deep, but as I see it, you have to ask if you want to redistribute it.

Using the excellent tutorial posted by liampetti as a starting point, you can create your own truly portable version as follows:
Modify the .properties file as described above.
Download and install the latest version of Python (3.6 at the time of writing)
Inside the PyCharm folder, copy the entire Python36 folder.
Create a new folder called 'App'
Inside 'App' create a new folder 'appinfo'
Use Portable IconExtract to extract the icons from the pycharm.exe file and place them in the appinfo folder
Rename any of the icons to 'appicon.ico'
create a new text file and rename it appinfo.ini
Add the following text:

[Format]
Type=PortableApps.comFormat
Version=3.2

[Control]
Start=pycharm.exe

Now comes the tricky part. You have to write your own launcher to place in the PyCharm folder, where PortableApps expects to see it.
Download and install SharpDevelop (free C# IDE which can also be made portable)
In a new console project use the following code:

using System;
using System.Threading;

namespace PyCharm_Portable_Launcher
{
	class Program
	{
		public static void Main(string[] args)
		{
			//full startup of .exe eg in .bin folder
			string AppPath = System.IO.Path.GetDirectoryName(System.Reflection.Assembly.GetExecutingAssembly().Location);
            AppPath = AppPath.Substring(0, AppPath.IndexOf(@"\PortableApps\"));        
			// IDE: 		X:\PortableApps\PyCharm\PyCharm Launcher\bin\Debug\PyCharm Launcher.exe
			// Compiled: 	X:\PortableApps\PyCharm\pycharm.exe (renamed)
			Console.WriteLine("Launching PyCharm\n\nHold tight!");
			try
			{
				System.Diagnostics.Process.Start(AppPath + @"\PortableApps\PyCharm\bin\pycharm.exe");
				Thread.Sleep(2000);
			}
			catch (Exception e)
			{
				Console.WriteLine(e.Message);
				Console.WriteLine("Press enter to exit");
				Console.ReadLine();
			}
		}
	}
}

In the project properties add the icon extracted earlier
Complile the project
rename the compiled .exe to pycharm.exe
copy it to the PyCharm Folder
You should now have an icon in PortableApps which starts your launcher, which in turn starts PyCharm
In PyCharm, add the local copy of Python.exe to the list and set as the default.