For one bucket of x elements,

1st requires 1 comparison
2nd requires 2 comparisons
3rd requires 3 comparisons
...
xth requires x comparisons

Total comparisons
= x + x-1 + ... + 2 + 1
= x(x+1)/2

If there are k buckets of n/k elements,
 
Total comparisons
= k * (n/k) * ((n/k)+1) / 2
= n(n + k)/2k