Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(i,K):
    for k in range(j,K):
      if memo[i][j] != 0:
        if memo[memo[i][j]-1][k] != 0:
          if i == j and j == k:
            s += memo[memo[i][j]-1][k]
          elif i == j or j == k or i == k:
            s += memo[memo[i][j]-1][k] * 3
          else:
            s += memo[memo[i][j]-1][k] * 6
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          if i == j and j == k:
            s += memo[memo[i][j]-1][k]
          elif i == j or j == k or i == k:
            s += memo[memo[i][j]-1][k] * 3
          else:
            s += memo[memo[i][j]-1][k] * 6
      else:
        memo[i][j] = math.gcd(i+1,j+1)
        memo[j][i] = memo[i][j]
        if memo[memo[i][j]-1][k] != 0:
          if i == j and j == k:
            s += memo[memo[i][j]-1][k]
          elif i == j or j == k or i == k:
            s += memo[memo[i][j]-1][k] * 3
          else:
            s += memo[memo[i][j]-1][k] * 6
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          if i == j and j == k:
            s += memo[memo[i][j]-1][k]
          elif i == j or j == k or i == k:
            s += memo[memo[i][j]-1][k] * 3
          else:
            s += memo[memo[i][j]-1][k] * 6
print(s)


Fixed submission:
import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(i,K):
    for k in range(j,K):
      if i == j and j == k:
        rate = 1
      elif i == j or j == k or i == k:
        rate = 3
      else:
        rate = 6
      s += math.gcd(math.gcd(i+1,j+1),k+1) * rate
print(s)

Buggy python submission (verdict: Runtime Error):
import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(i,K+1):
    for k in range(j,K+1):
      if memo[i][j] != 0:
        if memo[memo[i][j]-1][k] != 0:
          s += memo[memo[i][j]-1][k]
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          s += memo[k][memo[i][j]-1]
      else:
        
        memo[i][j] = math.gcd(i+1,j+1)
        memo[j][i] = memo[i][j]
        if memo[memo[i][j]-1][k] != 0:
          s += memo[memo[i][j]-1][k]
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          s += memo[k][memo[i][j]-1]
print(s)


Fixed submission:
import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(i,K):
    for k in range(j,K):
      if i == j and j == k:
        rate = 1
      elif i == j or j == k or i == k:
        rate = 3
      else:
        rate = 6
      s += math.gcd(math.gcd(i+1,j+1),k+1) * rate
print(s)

Buggy python submission (verdict: Time Limit Exceeded):

import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(K):
    for k in range(K):
      if memo[i][j] != 0:
        if memo[memo[i][j]-1][k] != 0:
          s += memo[memo[i][j]-1][k]
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          s += memo[k][memo[i][j]-1]
      else:
        
        memo[i][j] = math.gcd(i+1,j+1)
        memo[j][i] = memo[i][j]
        if memo[memo[i][j]-1][k] != 0:
          s += memo[memo[i][j]-1][k]
        else:
          memo[memo[i][j]-1][k] = math.gcd(memo[i][j],k+1)
          memo[k][memo[i][j]-1] = memo[memo[i][j]-1][k]
          s += memo[k][memo[i][j]-1]
print(s)

Fixed submission:
import numpy as np
import math
K = int(input())
memo = np.zeros((K,K),int)
s = 0
for i in range(K):
  for j in range(i,K):
    for k in range(j,K):
      if i == j and j == k:
        rate = 1
      elif i == j or j == k or i == k:
        rate = 3
      else:
        rate = 6
      s += math.gcd(math.gcd(i+1,j+1),k+1) * rate
print(s)