Buggy python submission (verdict: Time Limit Exceeded):
import math
K = int(input())
ans = 0
for a in range(1, K+1):
  for b in range(1, K+1):
    for c in range(1, K+1):
      ans += math.gcd(math.gcd(a, b), c)
print(ans)

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import math
# from itertools import product
from functools import reduce

def main():
    def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import math
from itertools import product
from functools import reduce

def main():
    def gcd(numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
    valiation = list(itertools.product(range(1, K+1), repeat=3))
    for v in valiation:
        ans += gcd(v)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import math
from itertools import product
from functools import reduce

def main():
    def gcd(numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
    valiation = list(itertools.product(range(1, K+1), repeat=3))
    for v in valiation:
        ans += gcd(v)
#     for i in range(1, K+1):
#         for j in range(1, K+1):
#             for k in range(1, K+1):
#                 ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import math
from itertools import product
from functools import reduce

def main():
    def gcd(numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
    valiation = list(itertools.product(range(1, K+1), repeat=3))
    for v in valiation:
        ans += gcd(v)
#     for i in range(1, K+1):
#         for j in range(1, K+1):
#             for k in range(1, K+1):
#                 ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import math
from itertools import product
from functools import reduce

def main():
    def gcd(numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
    valiation = list(itertools.product(range(1, K+1), repeat=3))
    for v in valiation:
        ans += gcd(v)
#     for i in range(1, K+1):
#         for j in range(1, K+1):
#             for k in range(1, K+1):
#                 ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

Fixed submission:
import math
# from itertools import product
from functools import reduce

def main():
#     def gcd(*numbers): return reduce(math.gcd, numbers)
    K = int(input())
    ans = 0
#     valiation = list(itertools.product(range(1, K+1), repeat=3))
#     for v in valiation:
#         ans += gcd(v)
    for i in range(1, K+1):
        for j in range(1, K+1):
            for k in range(1, K+1):
                ans += math.gcd(math.gcd(i, j), k)
    print(ans)
        
    
if __name__ == '__main__':
    main()