Buggy python submission (verdict: Time Limit Exceeded):
from math import gcd
k = int(input())
 
sum = 0
for x1 in range(1,k+1):
  for x2 in range(1,k+1):
    for x3 in range(1,k+1):
        ans = gcd(x3,gcd(x1,x2))
        sum += ans
 
print(sum)


Fixed submission:
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

for i in range(1,k+1):
  for j in range(1,k+1):
     if l[i][j] == -1:
        ans = fractions.gcd(i,j)
        l[i][j] = ans
        l[i][i] = ans
sum = 0
#1種類
for i in range(1,k+1):
  sum += i
#２種類
for i in range(1,k):
  for j in range(i+1,k+1):
    sum += l[i][j]*6

#3種類
for i in range(1,k-1):
  for j in range(i+1,k):
    for m in range(j+1,k+1):
      sum += l[l[i][j]][m]*6

print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
k = int(input())
 
sum = 0
for x1 in range(1,k+1):
  for x2 in range(1,k+1):
    for x3 in range(1,k+1):
      for i in range(1, 2):
        ans = fractions.gcd(x1,x2)
        ans = fractions.gcd(ans,x3)
        sum += ans
 
print(sum)

Fixed submission:
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

for i in range(1,k+1):
  for j in range(1,k+1):
     if l[i][j] == -1:
        ans = fractions.gcd(i,j)
        l[i][j] = ans
        l[i][i] = ans
sum = 0
#1種類
for i in range(1,k+1):
  sum += i
#２種類
for i in range(1,k):
  for j in range(i+1,k+1):
    sum += l[i][j]*6

#3種類
for i in range(1,k-1):
  for j in range(i+1,k):
    for m in range(j+1,k+1):
      sum += l[l[i][j]][m]*6

print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

sum = 0
for x1 in range(1,k+1):
  for x2 in range(1,k+1):
    for x3 in range(1,k+1):
      for i in range(1, 2):
        if l[x1][x2] == -1:
          ans = fractions.gcd(x1,x2)
          l[x1][x2] = ans
          l[x2][x1] = ans
        else:
          ans = l[x1][x2]
        if l[ans][x3] == -1:
          ans1 = fractions.gcd(ans,x3)
          l[ans][x3] = ans1 
          l[x3][ans] = ans1
        else:
          ans1 = l[ans][x3]
        
        sum += ans1
 
print(sum)

Fixed submission:
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

for i in range(1,k+1):
  for j in range(1,k+1):
     if l[i][j] == -1:
        ans = fractions.gcd(i,j)
        l[i][j] = ans
        l[i][i] = ans
sum = 0
#1種類
for i in range(1,k+1):
  sum += i
#２種類
for i in range(1,k):
  for j in range(i+1,k+1):
    sum += l[i][j]*6

#3種類
for i in range(1,k-1):
  for j in range(i+1,k):
    for m in range(j+1,k+1):
      sum += l[l[i][j]][m]*6

print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

sum = 0
for x1 in range(1,k+1):
  for x2 in range(1,k+1):
    for x3 in range(1,k+1):
      for i in range(1, 2):
        if l[x1][x2] == -1:
          ans = fractions.gcd(x1,x2)
        else:
          ans = l[x1][x2]
        if l[ans][x3] == -1:
          ans = fractions.gcd(ans,x3)
        else:
          ans = l[ans][x3]
        
        sum += ans
 
print(sum)

Fixed submission:
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

for i in range(1,k+1):
  for j in range(1,k+1):
     if l[i][j] == -1:
        ans = fractions.gcd(i,j)
        l[i][j] = ans
        l[i][i] = ans
sum = 0
#1種類
for i in range(1,k+1):
  sum += i
#２種類
for i in range(1,k):
  for j in range(i+1,k+1):
    sum += l[i][j]*6

#3種類
for i in range(1,k-1):
  for j in range(i+1,k):
    for m in range(j+1,k+1):
      sum += l[l[i][j]][m]*6

print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import fractions
k = int(input())

sum = 0
for x1 in range(1,k+1):
  for x2 in range(1,k+1):
    for x3 in range(1,k+1):
      for i in range(1, 2):
        ans = fractions.gcd(x1,x2)
        ans = fractions.gcd(ans,x3)
        sum += ans

print(sum)

Fixed submission:
import fractions
k = int(input())

l = [[-1 for _ in range(k+1)] for _ in range(k+1)]

for i in range(1,k+1):
  for j in range(1,k+1):
     if l[i][j] == -1:
        ans = fractions.gcd(i,j)
        l[i][j] = ans
        l[i][i] = ans
sum = 0
#1種類
for i in range(1,k+1):
  sum += i
#２種類
for i in range(1,k):
  for j in range(i+1,k+1):
    sum += l[i][j]*6

#3種類
for i in range(1,k-1):
  for j in range(i+1,k):
    for m in range(j+1,k+1):
      sum += l[l[i][j]][m]*6

print(sum)