output_description: Print the sum modulo 998244353.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      A_0\ A_1\ \cdots\ A_{N-1}
attempt: from collections import Counter
  
  MOD = 998244353
  n = int(input())
  a = list(map(int, input().split()))
  c = Counter(a)
  
  pws = [1 for _ in range(1000001)]
  for i in range(1, 1000001):
      pws[i] = (pws[i - 1] * 2) % MOD
  
  res = [0 for _ in range(1000001)]
  ans = 0
  
  for i in range(1000000, 0, -1):
      sum_of_sq, sq_of_sum = 0, 0
      for j in range(i, 1000001, i):
          sum_of_sq += pws[j] * c[j]
          sum_of_sq %= MOD
          sq_of_sum += j * c[j]
          sq_of_sum %= MOD
      sq_of_sum = pow(sq_of_sum, 2, MOD)
      res[i] = (sq_of_sum - sum_of_sq) * pow(2 * i, MOD - 2, MOD)
      res[i] %= MOD
      for j in range(2 * i, 1000001, i):
          res[i] -= res[j] * (j // i)
          res[i] %= MOD
      ans += res[i]
      ans %= MOD
  
  print(ans)
  
problem_description: Statement
  
  We have an integer sequence of length N: A_0,A_1,\cdots,A_{N-1}.
  
  Find the following sum (\mathrm{lcm}(a, b) denotes the least common multiple
  of a and b):
  
    * \sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j)
  
  Since the answer may be enormous, compute it modulo 998244353.
samples: [{"input": "3\n    2 4 6", "output": "22\n    \n\n\\mathrm{lcm}(2,4)+\\mathrm{lcm}(2,6)+\\mathrm{lcm}(4,6)=4+6+12=22.\n\n* * *"}, {"input": "8\n    1 2 3 4 6 8 12 12", "output": "313\n    \n\n* * *"}, {"input": "10\n    356822 296174 484500 710640 518322 888250 259161 609120 592348 713644", "output": "353891724"}]