A. Array Divisibility

An array of integers 𝑎1,𝑎2,⋯,𝑎𝑛 is beautiful subject to an integer 𝑘 if it satisfies the following:

• The sum of 𝑎𝑗 over all 𝑗 such that 𝑗 is a multiple of 𝑘 and 1≤𝑗≤𝑛, itself, is a multiple of 𝑘.
• More formally, if ∑𝑘|𝑗𝑎𝑗 is divisible by 𝑘 for all 1≤𝑗≤𝑛 then the array 𝑎 is beautiful subject to 𝑘. Here, the notation 𝑘|𝑗 means 𝑘 divides 𝑗, that is, 𝑗 is a multiple of 𝑘.

Given 𝑛, find an array of positive nonzero integers, with each element less than or equal to 10^5 that is beautiful subject to all 1≤𝑘≤𝑛.

It can be shown that an answer always exists.