how to remove repeating numbers from the table of random numbers?

I wrote a program that generates twenty random numbers. the chance of repeating the program is about 1/3. How can I rebuild my program? could anyone help me?

        for (int i = 0; i <= 19; i++) {
            rand[i] = (int) (Math.random() * 60 + 1);
        }
        for(int i=0;i<=19;i++)
        {
            rand_back[i]=rand[i];
        }

        for (int i = 0; i<=19;) {
            for(int j=0;j<=19;j++) {
                //porównaj czy wsytapiła juz taka sama liczba
                if((rand[i]==rand_back[j])&&(j!=i)) {
                    rand[j]=(int) (Math.random()*60+1);
                }
                if(j==19){
                    j=0;
                    i++;
                }
                if(i==19) {
                    break;
                }
            }
            if(i==19) {
                break;
            }
        }