output_description: Print the value \sum_{K=1}^N K\times f(K).
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
attempt: import sys
  
  read = sys.stdin.read
  readlines = sys.stdin.readlines
  from collections import defaultdict
  
  
  def main():
      n = int(input())
  
      maxa2 = (n + 1) // 2
      maxa2 = max(6, maxa2)  # maxa2が6未満だとエラーになる
      p = [
          False if i % 2 == 0 or i % 3 == 0 or i % 5 == 0 else True for i in range(maxa2)
      ]
      p[0] = p[1] = False
      p[2] = p[3] = p[5] = True
      for is1 in range(3, maxa2, 2):
          for is2 in range(is1**2, maxa2, is1):
              p[is2] = False
      prime_list = [i for i, b in enumerate(p) if b]
  
      nums = [i for i in range(n + 1)]
      prime_nums = {e: defaultdict(int) for e in range(n + 1)}
      for prime in prime_list:
          p = prime
          while p <= n:
              t1 = nums[p]
              jisu = 0
              while t1 > 1 and t1 % prime == 0:
                  jisu += 1
                  t1 = t1 // prime
              nums[p] = t1
              prime_nums[p][prime] = jisu
              p += prime
      r = 0
      for i, pre in enumerate(prime_nums.values()):
          t2 = i
          for v in pre.values():
              t2 *= v + 1
          r += t2
      print(r)
  
  
  if __name__ == "__main__":
      main()
  
problem_description: Statement
  
  For a positive integer X, let f(X) be the number of positive divisors of X.
  
  Given a positive integer N, find \sum_{K=1}^N K\times f(K).
samples: [{"input": "4", "output": "23\n    \n\nWe have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is 1\\times 1 +\n2\\times 2 + 3\\times 2 + 4\\times 3 =23.\n\n* * *"}, {"input": "100", "output": "26879\n    \n\n* * *"}, {"input": "10000000", "output": "838627288460105\n    \n\nWatch out for overflows."}]