The number is 10 + 1 per charisma point as written here
Successful settlements need four critical things: beds, food, water, and defense. In the same respect, power is required to meet these needs beyond the most basic sense, especially for defense. There is an easy and quick way to understand how much of each you need:
- Beds: One per settler (max of 10 settlers plus 1 settler per Charisma point).
- Food: One food per settler.
- Water: One water per settler.
- Defense: One point per settler, although more is more helpful.
- Power: Add all of the power consumption things you need running, that’s the required power.
As noted, you’ll probably have a max of 11 to 20 settlers, depending on your build.
So make sure you have enough water, food and defense with at least 1 charisma to get up to 11 and more.
So the max should be 21 as it is possible to get a SPECIAL over 10, with charisma at 11, that would make possible to have 21 settlers with the same amount of beds, food, water and defense.