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
Radical of an integer Radical of an integer In number theory, the radical of a positive integer "n" is defined as the product of the distinct prime numbers dividing "n". Each prime factor of "n" occurs exactly once as a factor of this product: The radical plays a central role in the statement of the abc conjecture. Radical numbers for the first few positive integers are For example, and therefore The function formula_4 is multiplicative (but not completely multiplicative). The radical of any integer "n" is the largest square-free divisor of "n" and so also described as the square-free kernel of "n". There is