Counting sort initialization of the output array, each take time. Therefore, the time for the whole algorithm is the sum of the times for these steps, . Because it uses arrays of length and , the total space usage of the algorithm is also . For problem instances in which the maximum key value is significantly smaller than the number of items, counting sort can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space . If each item to be sorted is itself an integer, and used as
Smooth number it is what the General number field sieve uses to build its notion of smoothness under the homomorphism formula_15. The On-Line Encyclopedia of Integer Sequences (OEIS) lists "B"-smooth numbers for small "B"s: Smooth number In number theory, a smooth (or friable) number is an integer which factors completely into small prime numbers. For example, a 7-smooth number is a number whose prime factors are all at most 7, so 49 = 7 and 15750 = 2 × 3 × 5 × 7 are both 7-smooth, while 11 and 702 = 2 × 3 × 13 are not. The term seems