Project Euler #29. What is wrong in my method? [on hold]

*Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

2^2=4, 2^3=8, 2^4=16, 2^5=32

3^2=9, 3^3=27, 3^4=81, 3^5=243

4^2=16, 4^3=64, 4^4=256, 4^5=1024

5^2=25, 5^3=125, 5^4=625, 5^5=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms: 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125 How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?*

My Solution

int main()
{
    vector <float> a;
    int count=0;
    float k;
    int size=100;
    count=(size-1)*(size-1);

// take the log of all the values and put them in an array

    for(int i=2;i<=size;i++)
        for(int j=2;j<=size;j++)
            a.push_back(k=i*log(j));

// sort the vector array

    sort(a.begin(),a.begin()+count);
    int distinct=count;

//check for duplicates, for each duplicate reduce 1 from total no. of elements

    for(int i=0;i<count;i++)
        if(a[i]==a[i+1])
            distinct--;

// Output distinct

    cout<<distinct<<endl;
    return 0;
}