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

Fixed submission:
from math import gcd

K = int(input())
out = 0
Count = [0]*K
gcds = [[0]*K for i in range(K)]

for i in range (1,K+1):
    for j in range(1,+K+1):
        value = gcd(i,j)
        gcds[i-1][j-1]=value
        Count[value-1]+=1

for i in range(1,K+1):
    for j in range(1,K+1):
        out +=gcds[i-1][j-1]*Count[j-1] #値*回数
        
print(out)

Buggy python submission (verdict: Runtime Error):
from math import gcd
K=int(input())+1
sum=0
for a in range(1,K):
    for b in range(1,K):
        for c in range(1,K):
            gcd1 = int(gcd(a,b))
            gcd2 = int(gcd(b,c))
            gcd = int(gcd(gcd1,gcd2))

            sum = sum+gcd
print(sum)

Fixed submission:
from math import gcd

K = int(input())
out = 0
Count = [0]*K
gcds = [[0]*K for i in range(K)]

for i in range (1,K+1):
    for j in range(1,+K+1):
        value = gcd(i,j)
        gcds[i-1][j-1]=value
        Count[value-1]+=1

for i in range(1,K+1):
    for j in range(1,K+1):
        out +=gcds[i-1][j-1]*Count[j-1] #値*回数
        
print(out)

Buggy python submission (verdict: Time Limit Exceeded):
import math
K=int(input())+1
sum=0
for a in range(1,K):
    for b in range(1,K):
        for c in range(1,K):
            gcd1 = int(math.gcd(a,b))
            gcd2 = int(math.gcd(b,c))
            gcd = int(math.gcd(gcd1,gcd2))

            sum = sum+gcd
print(sum)

Fixed submission:
from math import gcd

K = int(input())
out = 0
Count = [0]*K
gcds = [[0]*K for i in range(K)]

for i in range (1,K+1):
    for j in range(1,+K+1):
        value = gcd(i,j)
        gcds[i-1][j-1]=value
        Count[value-1]+=1

for i in range(1,K+1):
    for j in range(1,K+1):
        out +=gcds[i-1][j-1]*Count[j-1] #値*回数
        
print(out)

Buggy python submission (verdict: Time Limit Exceeded):
import math
K=int(input())
sum=0
for a in range(1,K+1):
    for b in range(1,K+1):
        for c in range(1,K+1):
            gcd1 = int(math.gcd(a,b))
            gcd2 = int(math.gcd(b,c))
            gcd = int(math.gcd(gcd1,gcd2))

            sum = sum+gcd
print(sum)

Fixed submission:
from math import gcd

K = int(input())
out = 0
Count = [0]*K
gcds = [[0]*K for i in range(K)]

for i in range (1,K+1):
    for j in range(1,+K+1):
        value = gcd(i,j)
        gcds[i-1][j-1]=value
        Count[value-1]+=1

for i in range(1,K+1):
    for j in range(1,K+1):
        out +=gcds[i-1][j-1]*Count[j-1] #値*回数
        
print(out)

Buggy python submission (verdict: Time Limit Exceeded):
import math
K=int(input())
sum=0
for a in range(1,K+1):
    for b in range(1,K+1):
        for c in range(1,K+1):
            gcd1 = int(math.gcd(a,b))
            gcd2 = int(math.gcd(b,c))
            
            #print(gcd1,gcd2)
            gcd = gcd1 = int(math.gcd(gcd1,gcd2))

            sum = sum+gcd
print(sum)

Fixed submission:
from math import gcd

K = int(input())
out = 0
Count = [0]*K
gcds = [[0]*K for i in range(K)]

for i in range (1,K+1):
    for j in range(1,+K+1):
        value = gcd(i,j)
        gcds[i-1][j-1]=value
        Count[value-1]+=1

for i in range(1,K+1):
    for j in range(1,K+1):
        out +=gcds[i-1][j-1]*Count[j-1] #値*回数
        
print(out)