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The resistor is needed to ensure that the mosfet turns itself off. The circuit will behave strange without it, like the mosfet latching on, or turning on by itself. 1 ohm is way too low value and will waste a lot of power. Instead, 10K is a very good common value for this, but you can use anything between 1k to 100k.
Optionally you can also put a resistor in series between the gate and the button if you like, ideally anything between 10 ohm to 100 ohm.
Optionally you can also put a resistor in series between the gate and the button if you like, ideally anything between 10 ohm to 100 ohm.