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: n = int(input())
  a = list(map(int, input().split()))
  MOD = 998244353
  
  max_a = max(a)
  c = [0] * (max_a + 1)
  for i in range(1, max_a + 1):
      c[i] = pow(i, MOD - 2, MOD)
  
  for i in range(1, max_a):
      j = i
      while True:
          j += i
          if j <= max_a:
              c[j] -= c[i]
              c[j] %= MOD
          else:
              break
  
  cnt = [0] * (max_a + 1)
  for i in range(n):
      cnt[a[i]] += 1
  
  ans = 0
  for i in range(1, max_a + 1):
      tmp0 = 0
      tmp1 = 0
      j = i
      while True:
          if j <= max_a:
              tmp0 += cnt[j] * j
              tmp1 += cnt[j] * (j**2)
          else:
              break
          j += i
      tmp0 *= tmp0
      ans += (tmp0 - tmp1) * c[i]
      ans %= MOD
  
  print((ans * pow(2, MOD - 2, MOD)) % MOD)
  
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"}]