Divisible Array (Codeforces 1828A)
Tags: Math, constructive algorithms

You are given a positive integer $$$n$$$. Please find an array $$$a_1, a_2, \ldots, a_n$$$ that is perfect.A perfect array $$$a_1, a_2, \ldots, a_n$$$ satisfies the following criteria:   $$$1 \le a_i \le 1000$$$ for all $$$1 \le i \le n$$$.  $$$a_i$$$ is divisible by $$$i$$$ for all $$$1 \le i \le n$$$.  $$$a_1 + a_2 + \ldots + a_n$$$ is divisible by $$$n$$$. 

Input: Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 200$$$). The description of the test cases follows.The only line of each test case contains a single positive integer $$$n$$$ ($$$1 \le n \le 200$$$) — the length of the array $$$a$$$.

Output: For each test case, output an array $$$a_1, a_2, \ldots, a_n$$$ that is perfect.We can show that an answer always exists. If there are multiple solutions, print any.

Note: In the third test case:   $$$a_1 = 1$$$ is divisible by $$$1$$$.  $$$a_2 = 2$$$ is divisible by $$$2$$$.  $$$a_3 = 3$$$ is divisible by $$$3$$$.  $$$a_1 + a_2 + a_3 = 1 + 2 + 3 = 6$$$ is divisible by $$$3$$$. In the fifth test case:   $$$a_1 = 3$$$ is divisible by $$$1$$$.  $$$a_2 = 4$$$ is divisible by $$$2$$$.  $$$a_3 = 9$$$ is divisible by $$$3$$$.  $$$a_4 = 4$$$ is divisible by $$$4$$$.  $$$a_5 = 5$$$ is divisible by $$$5$$$.  $$$a_1 + a_2 + a_3 + a_4 + a_5 = 3 + 4 + 9 + 4 + 5 = 25$$$ is divisible by $$$5$$$. 

Sample Inputs:
7
1
2
3
4
5
6
7

Sample Outputs:
1
2 4
1 2 3
2 8 6 4
3 4 9 4 5
1 10 18 8 5 36
3 6 21 24 10 6 14

Solution (Python):
def solve():
    n = int(input())
    a = [_ + 1 for _ in range(n)]
    if n % 2 == 0:
        a[0] = n // 2 + 1
    print(' '.join(list(map(str, a))))
for _ in range(int(input())):
    solve()

Solution (Python):
from sys import stdin, stdout
stdout.write('\n'.join((' '.join([str(num + num) for num in range(1, int(stdin.readline()) + 1)]) for _ in range(int(stdin.buffer.readline())))))

Solution (Python):
t = int(input())
for i in range(t):
    n = int(input())
    l1 = []
    if n % 2 == 1:
        for i in range(1, n + 1):
            l1.append(str(i))
        print(' '.join(l1))
    else:
        for i in range(1, n + 1):
            l1.append(str(2 * i))
        print(' '.join(l1))