Buggy python submission (verdict: Time Limit Exceeded):
import math
K = int(input())
t = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for k in range(1,K+1):
            t += math.gcd(math.gcd(i,j),k)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Runtime Error):
import math
K = int(input())
t = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for k in range(1,K+1):
            t += gcd(gcd(i,j),k)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Time Limit Exceeded):
import math
K = int(input())
t = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t += math.gcd(math.gcd(i,j),l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a
K = int(input())
t = 0
t1 = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t += gcd(gcd(i,j),l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a
K = int(input())
t = 0
t1 = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t = t + gcd(gcd(i,j),l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Time Limit Exceeded):
def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a
K = int(input())
t = 0
t1 = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t1 = gcd(i,j)
            t = t + gcd(t1,l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Runtime Error):
 def gcd(a,b):
    while b!=0:
        a,b=b,a%b
    return a
K = int(input())
t = 0
t1 = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t1 = gcd(i,j)
            t = t + gcd(t1,l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

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

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t = t + gcd(i,j,l)
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)

Buggy python submission (verdict: Time Limit Exceeded):
import math
K = int(input())
t = 0
for i in range(1,K+1):
    for j in range(1,K+1):
        for l in range(1,K+1):
            t1= math.gcd(i,j)
            t2 = math.gcd(t1,l)
            t = t + t2
print(t)

Fixed submission:
import math
from functools import reduce

def gcd(*numbers):
    return reduce(math.gcd, numbers)
K = int(input())
t = 0
t1 = 0
t2 = 0
for i in range(1,K+1):
    for j in range(i,K+1):
        for l in range(j,K+1):
            if i == j == l:
                t = t + i
            elif i == j or j ==l or l ==i:
                t = t + 3 * gcd(i, j,l)
            else:
                t = t + 6 * gcd(i,j,l)
             
           
           
print(t)