试除法求约数

public class Main {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        while(n -- > 0) {
            int x = in.nextInt();
            List<Integer> list = new ArrayList<>();
            for(int i = 1; i <= x / i; i ++) {
                if(x % i == 0) {
                    list.add(i);
                    if(x / i != i)
                        list.add(x / i);
                }
            }
            Collections.sort(list);
            for (Integer num : list) {
                System.out.print(num + " ");
            }
            System.out.println();
        }
    }
}

基本思想

数的乘积的约数个数

public class Main {
    private static final int N = 1000000007;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Map<Integer, Integer> map = new HashMap<>();
        int n = in.nextInt();
        while(n -- > 0) {
            int x = in.nextInt();
            for(int i = 2; i <= x / i; i ++) {
                while(x % i == 0) {
                    x /= i;
                    map.put(i,map.getOrDefault(i,0) + 1);
                }
            }
            if(x > 1)
                map.put(x,map.getOrDefault(x,0) + 1);
        }
        long res = 1;
        for (Integer value : map.values())
            res = res * (value + 1) % N;
        System.out.println(res);
    }
}

数的乘积的约数之和

public class Main {
    private static final int N = 1000000007;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Map<Integer, Integer> map = new HashMap<>();
        int n = in.nextInt();
        while(n -- > 0) {
            int x = in.nextInt();
            for(int i = 2; i <= x / i; i ++) {
                while(x % i == 0) {
                    x /= i;
                    map.put(i,map.getOrDefault(i,0) + 1);
                }
            }
            if(x > 1)
                map.put(x,map.getOrDefault(x,0) + 1);
        }
        long res = 1;
        for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
            long a = entry.getKey();
            long b = entry.getValue();
            long t = 1;
            while(b -- > 0)
                t = (t * a + 1) % N;
            res = res * t % N;
        }
        System.out.println(res);
    }
}

最大公约数