An interesting time complexity question

What is the time complexity of following function fun()? C

int fun(int n)
{    
    for (int i = 1; i <= n; i++)
    {
        for (int j = 1; j < n; j += i)
        {
            // Some O(1) task
        }
    }    
}

For i = 1, the inner loop is executed n times. For i = 2, the inner loop is executed approximately n/2 times. For i = 3, the inner loop is executed approximately n/3 times. For i = 4, the inner loop is executed approximately n/4 times. ............................................................. ............................................................. For i = n, the inner loop is executed approximately n/n times. So the total time complexity of the above algorithm is (n + n/2 + n/3 + ... + n/n) Which becomes n * (1/1 + 1/2 + 1/3 + ... + 1/n) The important thing about series (1/1 + 1/2 + 1/3 + ... + 1/n) is, it is equal to Θ(Logn) (See this for reference). So the time complexity of the above code is Θ(nLogn). As a side note, the sum of infinite harmonic series is counterintuitive as the series diverges. The value of is ∞. This is unlike geometric series as geometric series with ratio less than 1 converges. Reference: http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29#Rate_of_divergence http://staff.ustc.edu.cn/~csli/graduate/algorithms/book6/chap03.htm