Turn led on/off 20 times then remain off

Hi, I would like to turn an led on & off 20 times then it to remain off after the 20th time through the loop.
I am not sure what i am missing but hopefully a simple solution to the code.
hope some one can help.
i have attached the code.

const int ledPin =13;
int delayPeriod = 100;
int count =0;

void setup() {
pinMode (ledPin, OUTPUT);

}

void loop()
{
digitalWrite (ledPin, HIGH);
delay (delayPeriod);
digitalWrite (ledPin, LOW);
delay (delayPeriod);
count ++;
if (count == 20)
{
digitalWrite (ledPin, LOW);
}
}

    if (count <= 20)
   {
    digitalWrite (ledPin, HIGH);
    delay (delayPeriod);
    digitalWrite (ledPin, LOW);
    delay (delayPeriod);
    count ++;
    }

Thanks Shannon, that's exactly what i wanted.
Still trying to get my head around programming

Jimsjump:
Thanks Shannon,

“Shannon” is the respondent’s forum level, just as yours in “newbie”. His or her name is “aarg”.