Another solution, using the same logic but different structure. I was getting stuck with the type of sum variable, where I was using int. Then I come here and I saw this solution, tks to share it.

if(n.length() < 2) { return Character.getNumericValue(n.charAt(0)); }

    int count = 0;
    long sum = 0;
    while(count < n.length()) {
        sum += Character.getNumericValue(n.charAt(count));
        count++;
    }

    return superDigit(Long.toString(sum * k), 1);