TnT/Multi_CodeNet4Repair huggingface dataset:
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
K = int(input())
import math
import itertools


def better_gcd(a,b,c):
    tup = set((a,b,c))
    kinds = len(tup)
    if kinds == 3:
        return math.gcd(a, math.gcd(b, c)) * 6
    elif kinds == 2:
        return math.gcd(*tup) * 3
    else:
        return a

ans = 0
cands = list(itertools.combinations_with_replacement(range(1,201), 3))
for c in cands:
    ans += better_gcd(*c)
print(ans)

K = int(input())
import math
import itertools


def better_gcd(a,b,c):
    tup = set((a,b,c))
    kinds = len(tup)
    if kinds == 3:
        return math.gcd(a, math.gcd(b, c)) * 6
    elif kinds == 2:
        return math.gcd(*tup) * 3
    else:
        return a

ans = 0
cands = list(itertools.combinations_with_replacement(range(200), 3))
for c in cands:
    ans += better_gcd(*c)
print(ans)

import math

def better_gcd(a,b,c):
    tup = set((a,b,c))
    kinds = len(tup)
    if kinds == 3:
        return math.gcd(a, math.gcd(b, c)) * 6
    elif kinds == 2:
        return math.gcd(*tup) * 3
    else:
        return a

ans = 0
cands = list(itertools.combinations_with_replacement(range(200), 3))
for c in cands:
    ans += better_gcd(*c)
print(ans)

K = int(input())
import math
import itertools

def better_gcd(a,b,c):
    tup = set((a,b,c))
    kinds = len(tup)
    if kinds == 3:
        return math.gcd(a, math.gcd(b, c)) * 6
    elif kinds == 2:
        return math.gcd(*tup) * 3
    else:
        return a

ans = 0
cands = list(itertools.combinations_with_replacement(range(1,K+1), 3))
for c in cands:
    ans += better_gcd(*c)
print(ans)

Verdicts: Wrong Answer

Wrong Answer

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k=input()
sumk=0
for i in range (1,k+1):
    for a in range(1,k+1):
        for b in range(1,k+1):
            for c in range(1,k+1):
                gcd=1
                m=min(a,b,c)
                for x in range(1,m+1):
                    if (a%x==0 and b%x==0 and c%x==0):
                        gcd=x
                    else:
                        gcd=gcd
                        sumk=sumk+gcd
print(sumk)

k=int(input())
sumk=0
for i in range (1,k+1):
    for a in range(1,k+1):
        for b in range(1,k+1):
            for c in range(1,k+1):
                gcd=1
                m=min(a,b,c)
                for x in range(1,m+1):
                    if (a%x==0 and b%x==0 and c%x==0):
                        gcd=x
                    else:
                        gcd=gcd
                        sumk=sumk+gcd
print(sumk)

import math
k=int(input())
ans=0
for p in range(1,k+1):
    for q in range(1,k+1):
        gcd=math.gcd(p,q)
        for r in range(1,k+1):
            ans=ans+math.gcd(gcd,r)
print(ans)

Verdicts: Runtime Error

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import fractions

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 += fractions.gcd(fractions.gcd(a, b), c)

print(ans)

import fractions
 
k = int(input())
ans = 0
 
for a in range(1, k+1):
    for b in range(1, k+1):
        tmp = fractions.gcd(a, b)
        for c in range(1, k+1):
            ans += fractions.gcd(tmp, c)
 
print(ans)

import math
 
k = int(input())
ans = 0
 
for a in range(1, k+1):
    for b in range(1, k+1):
        tmp = math.gcd(a,b)
        for c in range(1, k+1):
            ans += math.gcd(tmp, c)
 
print(ans)

Verdicts: Time Limit Exceeded

Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from math import gcd
g=[201*[0]for _ in range(201)]
for i in range(1,201):
  for j in range(i,201):
    g[i][j]=gcd(i,j)
ans=0
for i in range(1,201):
  for j in range(1,201):
    for k in range(1,201):
    m=g[min(i,j)][max(i,j)]
    ans+=g[min(k,m)][max(k,m)]
print(ans)

from math import gcd
g=[201*[0]for _ in range(201)]
for i in range(1,201):
  for j in range(i,201):
    g[i][j]=gcd(i,j)
ans=0
for i in range(1,201):
  for j in range(i,201):
    anss=0
    for k in range(j,201):
      m=g[min(i,j)][max(i,j)]
      m=g[min(k,m)][max(k,m)]
      if k!=j:anss+=m
      anss+=m
    if i!=j:ans+=anss
    ans+=anss
print(ans)

from math import gcd
g=[201*[0]for _ in range(201)]
for i in range(1,201):
  for j in range(i,201):
    g[i][j]=gcd(i,j)
ans=0
for i in range(1,201):
  for j in range(1,201):
    for k in range(1,201):
      m=g[min(i,j)][max(i,j)]
      ans+=g[min(k,m)][max(k,m)]
print(ans)


def gcd(a,b):
  while b:a,b=b,a%b
  return a
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    x=gcd(i,j)
    for k in range(1,k+1):
      ans+=gcd(k,x)
print(ans)

Verdicts: Runtime Error

Wrong Answer

Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
K = int(input())
s = 0
for a in range(1,K+1):
  for b in range(1,K+1):
    x = math.gcd(a,b)
    for c in range(1,K+1):
      s += gcd(x,c)
print(s)

import math
K = int(input())
s = 0
for a in range(1,K+1):
  for b in range(1,K+1):
    x = math.gcd(a,b)
    for c in range(1,K+1):
      s += math.gcd(x,c)
print(s)


Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k = int(input())
sum=0
for a in range(1,k+1):
    for b in range(1,k+1):
        g1 = math.gcd(a,b)
        for c in range(1,k+1):
            sum += math.gcd(g1,c)
print(sum)

mod = 10**9 + 7
import math 
from bisect import bisect_left 
from collections import Counter
from itertools import combinations
 
def ain():
    return map(int, input().split())
def fain():
    return map(float, input().split())
 
def mc2(s):
    return (s*(s-1))//2 + s
    
# for tc in range(int(input())):
#     n = int(input())
    
#     print(ans)

k = int(input())
sum=0
for a in range(1,k+1):
    for b in range(1,k+1):
        g1 = math.gcd(a,b)
        for c in range(1,k+1):
            sum += math.gcd(g1,c)
print(sum)


Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
N=int(input())
S=input()
ans=S.count("R")*S.count("G")*S.count("B")
 
for i in range(N):
  for j in range(i+1,N):
    k=j+(j-i)
    if N-1<k:
      break
 
    if S[j]!=S[i] and S[j]!=S[k] and S[k]!=S[i]:
        ans-=1
        
print(ans)

from math import gcd
K=int(input())

result=[]
count=0
cnt=0


 
for i in range(1,K+1):
  for j in range(1,K+1):
    for k in range(1,K+1):
      cnt+=gcd(gcd(i,j),k)


print(cnt)



Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
N = int(input())
sum=0
import math
for i in range(N):
  for j in range(N):
       t=gcd(i+1,j+1)
       for k in range(N):
          sum =sum + gcd(t, k+1)
print(sum)


N = int(input())
sum=0
import math
from functools import reduce
def gcd(*numbers):
    return reduce(math.gcd, numbers)
from itertools import product
pools = product(N,N,N)
for i, j ,k in pools:
  sum =sum + gcd(i, j, k)

N = int(input())
sum=0
import math
from functools import reduce
def gcd(*numbers):
    return reduce(math.gcd, numbers)
from itertools import product
pools = product(range(N),range(N),range(N))
for i, j ,k in pools:
  sum =sum + gcd(i, j, k)
print(sum)

N = int(input())
sum=0
import math
for i in range(N):
  for j in range(N):
       t=math.gcd(i+1,j+1)
       for k in range(N):
          sum =sum + math.gcd(t, k+1)
print(sum)

Verdicts: Runtime Error

Runtime Error

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from itertools import product

def gcb(a, b):
    if b == 0:
        return a
    return gcb(b, a % b)

def gcb_3(a, b, c):
    return gcb(gcb(a, b), gcb(b, c))

k = int(input())
res = 0
l_k = range(1, k+1)
for part in itertools.product(l_k, l_k, l_k):
    res += gcb_3(part[0], part[1], part[2])
print(res)

from itertools import product
 
def gcb(a, b):
    if b == 0:
        gcb_table[a][b] = a
    else:
        if gcb_table[a][b] == -1:
            gcb_table[a][b] = gcb(b, a%b)
    return gcb_table[a][b]

def gcb_3(a, b, c):
    return gcb(gcb(a, b), gcb(b, c))
  
k = int(input())
gcb_table = [[-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):
        temp = gcb(i, j)
        gcb_table[i][j] = temp
        gcb_table[j][i] = temp
        
res = 0
l_k = range(1, k+1)
for part in itertools.product(l_k, l_k, l_k):
    gcb_first = gcb_table[part[0]][part[1]]
    res += gcb_table[gcb_first][part[2]]
print(res)

from itertools import product
 
def gcb(a, b):
  	if a < b:
      	a, b = b, a
    if b == 0:
        gcb_table[a][b] = a
    else:
        if gcb_table[a][b] == -1:
            gcb_table[a][b] = gcb(b, a%b)
    return gcb_table[a][b]
  
k = int(input())
gcb_table = [[-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):
        temp = gcb(i, j)
        gcb_table[i][j] = temp
        gcb_table[j][i] = temp
        
res = 0
l_k = range(1, k+1)
for part in itertools.product(l_k, l_k, l_k):
    gcb_first = gcb_table[part[0]][part[1]]
    res += gcb_table[gcb_first][part[2]]
print(res)

from itertools import product
 
def gcb(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        gcb_table[a][b] = a
    else:
        if gcb_table[a][b] == -1:
            gcb_table[a][b] = gcb(b, a%b)
    return gcb_table[a][b]

k = int(input())
gcb_table = [[-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):
        temp = gcb(i, j)
        gcb_table[i][j] = temp
        gcb_table[j][i] = temp
        
res = 0
l_k = range(1, k+1)
for part in itertools.product(l_k, l_k, l_k):
    gcb_first = gcb_table[part[0]][part[1]]
    res += gcb_table[gcb_first][part[2]]
print(res)

def gcb(a, b):
    if a < b:
        a, b = b, a
    if b == 0:
        gcb_table[a][b] = a
    else:
        if gcb_table[a][b] == -1:
            gcb_table[a][b] = gcb(b, a%b)
    return gcb_table[a][b]

k = int(input())
gcb_table = [[-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):
        temp = gcb(i, j)
        gcb_table[i][j] = temp
        gcb_table[j][i] = temp
        
res = 0
for a in range(1, k+1):
    for b in range(1, k+1):
        gcb_first = gcb_table[a][b]
        for c in range(1, k+1):
            res += gcb_table[gcb_first][c]
print(res)

Verdicts: Runtime Error

Runtime Error

Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
x = np.arange(1, K + 1)
nums = np.gcd.outer(np.gcd.outer(x, x), x)

import numpy as np
 
K=int(input())
 
x = np.arange(1, K + 1)
nums = np.gcd.outer(np.gcd.outer(x, x), x)
print(nums.sum())

Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math

K = int(input())
sum = 0

for i in (1, K + 1):
  for j in range(1, K + 1):
    a = math.gcd(i, j)
    for k in range(1, K + 1):
      sum += math.gcd(a, k)
      
print(sum)


import math

K = int(input())
sum = 0

for i in (1, K + 1):
  for j in range(1, K + 1):
    tmp = math.gcd(i, j)
    for k in range(1, K + 1):
      sum += math.gcd(tmp, k)
      
print(sum)


import math

K = int(input())
sum = 0

for i in (1, K + 1):
  for j in range(1, K + 1):
    for k in range(1, K + 1):
      sum += math.gcd(i, j, k)
      
print(sum)

import math

K = int(input())
sum = 0

for i in (1, K + 1):
  for j in range(1, K + 1):
    a = math.gcd(i, j)
    for k in range(1, K + 1):
      sum += math.gcd(a, k)
      
print(sum)


import math

K = int(input())
sum = 0

for i in (1, K + 1):
  for j in range(1, K + 1):
    a = math.gcd(i, j)
    
    if a == 1:
      sum += a * K
      
    else:
      for k in range(1, K + 1):
        sum += math.gcd(a, k)
      
print(sum)


import math

K = int(input())
sum = 0

for i in range(1, K + 1):
  for j in range(1, K + 1):
    tmp = math.gcd(i, j)
    for k in range(1, K + 1):
      sum += math.gcd(tmp, k)
      
print(sum)


Verdicts: Wrong Answer

Wrong Answer

Runtime Error

Wrong Answer

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
s = input()
k = int(s)
n = 3
ans={}
for i in reversed(range(1, k+1)):
    ans[i]=math.floor(k/i)**n
    l=2
    j=i*l
    while j<=k:
        ans[i]=ans[i]-ans[j]
        l +=1
        j = i*l
res=0
for i in ans:
    res+=i*ans[i]
print(res)

s = input().split()
k = int(s[0])
n = 3
ans={}
for i in reversed(range(1, k+1)):
    ans[i]=math.floor(k/i)**n
    l=2
    j=i*l
    while j<=k:
        ans[i]=ans[i]-ans[j]
        l +=1
        j = i*l
res=0
for i in ans:
    res+=i*ans[i]
print(res)

s = input()
k = int(s)
n = 3
ans={}
for i in reversed(range(1, k+1)):
    ans[i]=math.floor(k/i)**n
    l=2
    j=i*l
    while j<=k:
        ans[i]=ans[i]-ans[j]
        l +=1
        j = i*l
res=0
for i in ans:
    res+=i*ans[i]
print(res)

s = input().split()
k = int(s[0])
n = 3
ans={}
for i in reversed(range(1, k+1)):
    # print(i*(math.floor(k/i))**n)
    ans[i]=math.floor(k/i)**n
    l=2
    j=i*l
    while j<=k:
        ans[i]=ans[i]-ans[j]
        l +=1
        j = i*l
res=0
for i in ans:
    res+=i*ans[i]
print(res)

import math
s = input()
k = int(s)
n = 3
ans={}
for i in reversed(range(1, k+1)):
    ans[i]=math.floor(k/i)**n
    l=2
    j=i*l
    while j<=k:
        ans[i]=ans[i]-ans[j]
        l +=1
        j = i*l
res=0
for i in ans:
    res+=i*ans[i]
print(res)

Verdicts: Runtime Error

Runtime Error

Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
K=int(input())
ans=0
 
import math
 
for i in range(1,K+1):
  for j in range(1,K+1):
    x = math.gcd(i,j)
    for k in range(1,K+1):
      ans += math.gcd(x,j)

print(ans)

K=int(input())
ans=0
 
import math
 
for i in range(1,K+1):
  for j in range(1,K+1):
    x = math.gcd(i,j)
    for k in range(1,K+1):
      ans += math.gcd(x,k)

print(ans)

Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k = int(input())
k = [int(x)+1 for x in range(k)]
#print(k)
from fractions import gcd
from itertools import product,combinations
from functools import reduce
num = 0

for v in product(k,repeat =3):
    v = (list(v))
    
    a = reduce(gcd,v)
    num +=a
    #print(v,num)
print(num)

k = int(input())
import math
num = 0
for i in range(1,k+1):
    for j in range(1,k+1):
        a = math.gcd(i,j)
        for l in range(1,k+1):
            b = math.gcd(a,l)
            num += b
print(num)

Verdicts: Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import fractions
K=int(input())
total = 0

for a in range(K):
  for b in range(a,K):
    for c in range(b,K):
      total += fractsion.gcd(a+1, fractions.gcd(b+1,c+1) )
total *= 6

for a in range(K):
  for b in range(a,K):
    total += fractions.gcd(a+1, b+1)
total *= 6

for a in range(K):
  total += (a+1)

print(total)

import math
K=int(input())
total = 0

for a in range(1,K+1):
  for b in range(a+1,K+1):
    for c in range(b+1,K+1):
      total += math.gcd(a, math.gcd(b,c) ) * 6
      
for a in range(1,K+1):
  for b in range(a+1,K+1):
    total += math.gcd(a, b)*6

for a in range(1,K+1):
  total += a

print(total)


Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
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 j in range(1, K+1):
#             for k in range(1, K+1):
#                 ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

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()

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 j in range(1, K+1):
#             for k in range(1, K+1):
#                 ans += gcd(i, j, k)
    print(ans)
        
    
if __name__ == '__main__':
    main()

import math
# from itertools import product
from functools import reduce

def main():

    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(i, K+1):
            for k in range(j, K+1):
                x = math.gcd(math.gcd(i, j), k)
                if i == j == k:
                    ans += x
                elif i != j and j != k and k != i:
                    ans += 6 * x
                else:
                    ans += 3 * x
    print(ans)
        
    
if __name__ == '__main__':
    main()

Verdicts: Runtime Error

Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math

ans = 0
k = int(input())
for a in range(k):
    for b in range(k):
        tmp = math.gcd(a, b)
        for c in range(k):
            ans += math.gcd(tmp, c)

print(ans)


import math
k = int(input())

ans = 0
for a in range(1, k+1):
    for b in range(1, k+1):
        tmp = math.gcd(a, b)
        for c in range(1, k+1):
            ans += math.gcd(tmp, c)
print(ans)


Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from math import gcd

def solve():
    K = int(input())
    ans = 0
    
    for i in range(1,K+1):
        num = [0, 0, 0]
        num[0] = i
        for k in range(1,K+1):
            num[1] = k
            for m in range(1,K+1):
                num[2] = m
                ans += reduce(gcd, num)
    return ans

print(solve())

from math import gcd

def solve():
    K = int(input())
    ans = 0

    for i in range(1,K+1):
        for k in range(1,K+1):
            b = gcd(i, k)
            for m in range(1,K+1):
                ans += gcd(b, m)
    return ans

print(solve())



Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
def main():
    k = int(input())
    k1 = k + 1

    sum = 0
    for i in range(1, k1):
        for j in range(1, k1):
            for m in range(1, k1):
                sum += math.gcd(math.gcd(i, j), m)
    print(sum)

main()

import math


def main():
    k = int(input())
    k1 = k + 1

    sum = 0
    for i in range(1, k1):
        for j in range(1, k1):
            for m in range(1, k1):
                sum += math.gcd(math.gcd(i, j), m)
    print(sum)

main()



Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k=int(input())
ans=0
from math import gcd
for a in range(1,201):
  for b in range(1,201):
    for c in range(1,201):
      ans+=gcd(gcd(a,b),c)
print(ans)

k=int(input())
ans=0
from math import gcd
for a in range(1,k+1):
  for b in range(1,k+1):
    for c in range(1,k+1):
      ans+=gcd(gcd(a,b),c)
print(ans)

Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
def sort_2(a,b):
    if b<a:
        c=a
        a=b
        b=c
    return [a,b]


def GCDbase(a,b):
    D=b//a
    if b==D*a:
        return a
    else:
        return GCD(b-a*D,a)
    
def GCD(a,b):
    ab=sort_2(a,b)
    return GCDbase(ab[0],ab[1])
    
    

K=int(input())
sum=0
for i in range(1,K+1):
    for j in range(1,K+1):
	t=GCD(i,j)
        for l in range(1,K+1):

            sum+=GCD(t,l)
print(sum)

import math
K=int(input())
sum=0
for i in range(1,K+1):
    for j in range(1,K+1):
        tmp=math.gcd(i,j)
        for l in range(1,K+1):
            sum+=math.gcd(tmp,l)
print(sum)


Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from math import gcd
k=int(input())
ans=0
for i in range(0,k):
  for j in range(0,k):
    for l in range(0,k):
      ans=ans+gcd(gcd(i,j),l)
print(ans)


import fractions
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    for l in range(1,k+1):
      ans=ans+fractions.gcd(i,fractions.gcd(j,l))
print(ans)

from fractions import gcd
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    for l in range(1,k+1):
        a=(i,j,l)
        if len(a)==1:
            ans=ans+i
        elif len(a)==2:
            ans=ans+fractions.gcd(a[0],a[1])
        else:
            ans=ans+fractions.gcd(a[0],fractions.gcd(a[1],a[2]))
print(ans)

from fractions import gcd
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    for l in range(1,k+1):
        a=(i,j,l)
        if len(a)==1:
            ans=ans+i
        elif len(a)==2:
            ans=ans+gcd(a[0],a[1])
        else:
            ans=ans+gcd(a[0],gcd(a[1],a[2]))
print(ans)


from math import gcd
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    for l in range(1,k+1):
      ans=ans+gcd(gcd(i,j),l)
print(ans)

Verdicts: Wrong Answer

Time Limit Exceeded

Runtime Error

Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k = int(input())
import math
k1 = 0
k2 = 0
k3 = 0
count = 0
for i in range(0,k):
  k1 = k1 + 1
  for j in range(0,i):
    k2 = k2 + 1
    for k in range(0, j):
      k3 = k3 + 1
      if k1==k2==k3:
        count = count + k1
      elif k1==k2 or k2==k3 or k3==k1:
        count = count + 3*math.gcd(k1,k2,k3)
      else:
        count = count + 6*math.gcd(k1,k2,k3)

k = int(input())
import math
k1 = 0
k2 = 0
k3 = 0
count = 0
for i in range(0,k):
  k1 = k1 + 1
  k2 = 0
  for j in range(0,k1):
    k3=0
    k2 = k2 + 1
    for k in range(0, k2):
      k3 = k3 + 1
      if k1==k2==k3:
        count = count + k1
      elif k1==k2:
        count = count + 3*math.gcd(k1,k3)
      elif k2==k3:
        count = count + 3*math.gcd(k1,k2)
      elif k3==k1:
        count = count + 3*math.gcd(k1,k2)
      else:
        k4 = math.gcd(k1,k2)
        count = count + 6*math.gcd(k3,k4)
print(count)
print(k1,k2,k3)


k = int(input())
import math
k1 = 0
k2 = 0
k3 = 0
count = 0
for i in range(0,k):
  k1 = k1 + 1
  k2 = 0
  for j in range(0,k1):
    k3=0
    k2 = k2 + 1
    for k in range(0, k2):
      k3 = k3 + 1
      if k1==k2==k3:
        count = count + k1
      elif k1==k2:
        count = count + 3*math.gcd(k1,k3)
      elif k2==k3:
        count = count + 3*math.gcd(k1,k2)
      elif k3==k1:
        count = count + 3*math.gcd(k1,k2)
      else:
        k4 = math.gcd(k1,k2)
        count = count + 6*math.gcd(k3,k4)
print(count)


Verdicts: Runtime Error

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7
import numpy as np
 
K = INT()
sum = 0
 
for n in range(K):
  for m in range(K):
    for l in range(K):
      sum += gcd(n+1, gcd(m+1, l+1))
 
print(sum)

from math import  gcd

K = INT()
sum = 0
 
for n in range(K):
  for m in range(K):
    for l in range(K):
      sum += gcd(n+1, gcd(m+1, l+1))
 
print(sum)

import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, gcd
from itertools import accumulate, permutations, combinations, product, groupby
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from heapq import heappush, heappop
from functools import reduce
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7
import numpy as np
 
K = INT()
sum = 0
 
for n in range(1, K+1):
  for m in range(1, K+1):
    sum1 = gcd(n, m)
    for l in range(1, K+1):
      sum += gcd(l, sum1)
 
print(sum)

Verdicts: Time Limit Exceeded

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math

K = int(input())

sum = 0
for i in range(K):
    for j in range(K):
        for k in range(K):
            sum += math.gcd(math.gcd(i, j), k)
            
print(sum)

import math
 
K = int(input())
 
sum = 0
for i in range(K):
    for j in range(K):
        r = math.gcd(i+1, j+1)
        for k in range(K):
            sum += math.gcd(r, k+1)
            
print(sum)


Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from fractions import gcd 
from functools import reduce
import itertools
k = int(input())
a = [i for i in range(1,k+1)]
s = 0
for t in itertools.product(a,repeat=3):
  s += reduce(gcd,t)
print(s)

from fractions import gcd 
from functools import reduce
import itertools
k = int(input())
a = [i for i in range(1,k+1)]
s =0

s = int(k*(k+1)/2)

for q in itertools.combinations(a,2):
  s += reduce(gcd,q)*3*2
for t in itertools.combinations(a,3):
  s += reduce(gcd,t)*6
print(s)

import math
from functools import reduce
import itertools
k = int(input())
a = [i for i in range(1,k+1)]
s =0

s = int(k*(k+1)/2)

for q in itertools.combinations(a,2):
  s += reduce(math.gcd,q)*3*2
for t in itertools.combinations(a,3):
  s += reduce(math.gcd,t)*6
print(s)

Verdicts: Time Limit Exceeded

Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
def gcd(*numbers):
    return reduce(math.gcd, numbers)

def gcd_list(numbers):
    return reduce(math.gcd, numbers)

line = int(input())

a = list(range(1,line + 1))
b = list(range(1,line + 1))
c = list(range(1,line + 1))

result = list(itertools.product(a,b,c))

all = 0

for i in result:
    tmp = gcd(i[0], i[1], i[2])
    all += tmp

print(all)

from math import gcd

line = int(input())

ans = 0

for a in range(1, line + 1):
    for b in range(1, line + 1):
        c = gcd(a,b)
        for d in range(1, line + 1):
            ans += gcd(d,c)
print(ans)

Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
n = int(input() )

sum = 0
for i in range (1,n):
    for j in range (1,n): 
        for k in range (1,n):
            sum += math.gcd(  math.gcd(i,j) ,k )
            

print( sum )

import math
n = int(input() )
n+=1
sum = 0
for i in range (1,n):
    for j in range (1,n):
        gcdIJ = math.gcd(i,j)
        for k in range (1,n):
            sum += math.gcd( gcdIJ  ,k )
            #print(i,j,k)

print( sum )

Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
from functools import reduce
import itertools


def gcd_list(numbers):
  return reduce(math.gcd, numbers)


k = int(input())
items = list(range(1, k+1))
ans = 6 * sum(items)
ans += sum([6 * gcd_list(item) for item in itertools.combinations(items, 2)])
ans += sum([6 * gcd_list(item) for item in itertools.combinations(items, 3)])

print(ans)



import math
from functools import reduce
import itertools


def gcd_list(numbers):
  return reduce(math.gcd, numbers)


k = int(input())
items = list(range(1, k+1))
ans = sum(items)
ans += sum([6 * gcd_list(item) for item in itertools.combinations(items, 2)])
ans += sum([6 * gcd_list(item) for item in itertools.combinations(items, 3)])

print(ans)



Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
K = int(input())
print(K ** 3 + (1 / 2) *K ** 2 - (1 / 2) * K)

import math

k = int(input())
sum = 0

for i in range(1, k + 1):
    for j in range(1, k + 1):
        sum1 = math.gcd(i , j)
        for l in range(1, k + 1):
            sum += math.gcd(sum1, l)
print(sum)


Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
a = int(input())
l = []
def gcd(n, m):
    if m == 0:
        return n
    else:
        return gcd(m, n%m)
    for n in range(1, a+1):
        for m in range(a+1):
            for p in range(1, a+1):
                ans = gcd(n, gcd(m, p))
                l.append(ans)
print(sum(l))

from math import gcd
a = int(input())
ans = 0 
for i in range(1, a+1):
    for j in range(1, a+1):
        for k in range(1, a+1):
            ans += gcd(gcd(i,j),k)
print(ans)

Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
from functools import reduce
def gcd(*number):
    return reduce(math.gcd, number)
n = int(input())
a, b, c = 1, 1, 1
sum = 0
list_number = []
while True:
    print(a,b,c)
    list_number.append(gcd(a, b, c))
    if n > c:
        c += 1
    elif n == c and n == b and n == a:
        break
    elif n == c and n == b:
        a += 1
        b = 1
        c = 1
    elif n == c:
        b += 1
        c = 1
for i in list_number:
    sum = sum + i
print(sum)

import math
from functools import reduce
def gcd(*number):
    return reduce(math.gcd, number)
n = int(input())
a, b, c = 1, 1, 1
sum = 0
list_number = []
while True:
    print(a,b,c)
    list_number.append(gcd(a, b, c))
    if n > c:
        c += 1
    elif n == c and n == b and n == a:
        break
    elif n == c and n == b:
        a += 1
        b = 1
        c = 1
    elif n == c:
        b += 1
        c = 1
print(list_number)
for i in list_number:
    sum = sum + i
print(sum)

from math import gcd
n = int(input())
sum = 0
for i in range(1, n + 1):
    for j in range(1, n + 1):
        for k in range(1, n + 1):
            sum += gcd(gcd(i, j), k)
print(sum)

Verdicts: Wrong Answer

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import numpy as np
k=int(input())
s=0
n=range(k+1)
for x,y,z in n:
	s+=np.gcd.reduce([x,y,z])
print(s)

import math
k=input()
s=0
for x in range(1,k+1):
  for y in range(1,k+1):
    for z in range(1,k+1):
      s+=math.gcd(x,gcd(y,z))
print(s)

import math
k=int(input())
l=[]
s=0
for x in range(1,k+1):
  for y in range(1,k+1):
    l.append(math.gcd(x,y))

for x in range(len(l)):
  for y in range(1,k+1):
    s+=math.gcd(l[x],y)
print(s)

Verdicts: Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import numpy as np
K = int(input())
a = np.arange(a,K+1)
b = np.gcd.outer(np.gcd.outer(a, a), a)
print(np.sum(b))


from numpy import gcd
N = int(input())
a = np.arange(1,N+1)
b = np.gcd.outer(np.gcd.outer(a,a), a)
print(b)

import numpy as np
K = int(input())
a = np.arrange(a,K+1)
b = np.gcd.outer(np.gcd.outer(a, a), a)
print(np.sum(b))

import numpy as np
K = int(input())
a = np.arange(1,K+1)
b = np.gcd.outer(np.gcd.outer(a, a), a)
print(np.sum(b))

Verdicts: Runtime Error

Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
from functools import reduce

K = int(input())
sum = 0

def gcd(*numbers):
    return reduce(math.gcd, numbers)

for i in range(K):
    for j in range(K):
        tmp = math.gcd(i+1, j+1)
        for k in range(K):
            sum += gcd(g, k+1)
        
print(sum)


import math

K = int(input())
sum = 0

for i in range(K):
    for j in range(K):
        tmp = math.gcd(i+1, j+1)
        for k in range(K):
            sum += math.gcd(tmp, k+1)
        
print(sum)


Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
 
K = int(input())
 
_sum = 0
 
for a in range(1, K):
    for b in range(1, K):
        for c in range(1, K):
            _sum += math.gcd(math.gcd(a, b), c)
print(_sum)

import math

K = int(input())

_sum = 0
for a in range(1, K):
    for b in range(1, K):
        for c in range(1, K):
            _sum += math.gcd(math.gcd(a, b), c)*6
print(_sum)

import math

K = int(input())

_sum = 0
_sum = sum([i for i in range(1, K)])
_sum += sum([sum([math.gcd(i, j)*6 for i in range(j+1, K)]) for j in range(1, K)])

for a in range(1, K):
    for b in range(a+1, K):
        for c in range(b+1, K):
            _sum += math.gcd(math.gcd(a, b), c)
print(_sum)

import math

K = int(input())

_sum = 0

for a in range(1, K):
    for b in range(a+1, K):
        for c in range(b+1, K):
            _sum += math.gcd(math.gcd(a, b), c)
print(_sum)

import math

K = int(input())

_sum = 0
_sum = sum([i for i in range(1, K+1)])
_sum += sum([sum([math.gcd(i, j)*6 for i in range(j+1, K+1)]) for j in range(1, K+1)])

for a in range(1, K+1):
    for b in range(a+1, K+1):
        for c in range(b+1, K+1):
            _sum += math.gcd(math.gcd(a, b), c)*6
print(_sum)


Verdicts: Wrong Answer

Wrong Answer

Wrong Answer

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
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)

 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)

from math import gcd

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)

Verdicts: Runtime Error

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from math import gcd

def solv():
    n = int(input())
    ans = 0
    for i in range(1, n + 1):
        for j in range(1, n + 1):
            a = gcd(i, j)
            for k in range(1, n + 1):
                ans += gcd(a, k)
    print(ans)

solve()

import sys
import numpy as np

from math import gcd

N = int(sys.stdin.readline())
ans = 0
"""
dp = np.zeros((N+1, N+1))
def gcd(a, b):
    if a < b:
        a, b = b, a
    
    if dp[a][b] != 0:
        return dp[a][b]

    while b>0:
        a, b = b, a % b
    
    dp[a][b] = a
    return a
"""
for i in range(1,N+1):
    for j in range(1,N+1):
        temp = gcd(i, j)
        for k in range(1,N+1):
            ans += gcd(temp, k)
            
print(ans)

Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k=int(input())
import fractions
ans=0
for i in range(1,k+1):
    for j in range(1,k+1):
        an=fractions.gcd(i,j)
        for s in range(1,k+1):
            anse=fractions.gcd(s,an)
            ans+=anse
print(ans)

k=int(input())

ans=0
for i in range(1,k+1):
    for j in range(1,k+1):
        an=fractions.gcd(i,j)
        for s in range(1,k+1):
            anse=fractions.gcd(s,an)
            ans+=anse
print(ans)

k=int(input())
from math import gcd
ans=0
for i in range(1,k+1):
    for j in range(1,k+1):
        for s in range(1,k+1):
            ans+=gcd(gcd(i,j),s)
print(ans)


Verdicts: Time Limit Exceeded

Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math


def gcd(a, b, c):
  d = math.gcd(a, b)
  return math.gcd(c, d)

K = int(input())
sum = 0

for i in range(1, a+1):
  for j in range(1, b+1):
    for k in range(1, c+1):
      sum += gcd(i, j, k)
      
print(sum)

import math
 
 
def gcd(a, b, c):
  d = math.gcd(a, b)
  return math.gcd(c, d)
 
K = int(input())
sum = 0
for i in range(1, K+1):
  sum += gcd(i, i, i)
  
for i in range(1, K+1):
  for j in range(i, K+1):
    for k in range(j, K+1):
      if i == j and j == k:
        sum += 0
      elif i == j or j == k or i == k:
        sum += gcd(i , j , k )*3
      elif i != j and j != k :
        sum += gcd(i, j, k)*6

print(sum)

Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from fractions import gcd
n=int(input())
cnt=0
for i in range(1,n+1):
  for j in range(1,n+1):
    a=gcd(i,j)
    for k in range(1,n+1):
      cnt+=gcd(a,k)
print(cnt)


from fractions import gcd
k=int(input())
cnt=0
for i in range(1,k+1):
  for j in range(1,k+1):
    a=gcd(i,j)
    for k in range(1,k+1):
      cnt+=gcd(a,k)
print(cnt)

from math import gcd
k=int(input())
cnt=0
for i in range(1,k+1):
  for j in range(1,k+1):
    a=gcd(i,j)
    for k in range(1,k+1):
      cnt+=gcd(a,k)
print(cnt)


Verdicts: Time Limit Exceeded

Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import fractions
from functools import reduce
import itertools

def gcd(*numbers):
    return reduce(fractions.gcd, numbers)
  
K = int(input())

ans = 0
for comb in itertools.product(range(1, K+1), repeat=3):
    ans += gcd(*comb)

print(ans)


import fractions
from functools import reduce
import itertools
import math

def gcd(*numbers):
    return reduce(math.gcd, numbers)

K = int(input())

if K == 1:
    ans = 1
elif K == 2:
    ans = 9
else:
    ans = 0
    for i in range(1, K+1):
        ans += i
        for j in range(i+1, K+1):
            ans += gcd(i, j) * 6
            for k in range(j+1, K+1):
                ans += gcd(i, j, k) * 6

print(ans)


Verdicts: Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
def gud(a,b):
  if a%b==0:
    return b
  else:
    return gud(b,a%b)
a=int(input())
ans=0
for i in range(1,a+1):
  for j in range(1,a+1):
    n=math.gcd(i+1,j+1)
    for k in range(1,a+1):
      ans+=math.gcd(n,k+1)
print(ans)

import math
def gud(a,b):
  if a%b==0:
    return b
  else:
    return gud(b,a%b)
a=int(input())
ans=0
for i in range(1,a+1):
  for j in range(1,a+1):
    n=math.gcd(i,j)
    for k in range(1,a+1):
      ans+=math.gcd(n,k)
print(ans)

Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
k=int(input())
f=0
g=0
h=0
import math
for a in range(1,k+1):
    for b in range(1,a+1):
        for c in range(1,b):
            d=math.gcd(a,b)
            e=math.gcd(d,c)
            f+=e
for a in range(1,k+1):
    for b in range(1,a):
        for c in range(1,b):
            d=math.gcd(a,b)
            e=math.gcd(d,c)
            g+=e
h=int((1+k)*k/2)
i=h+((f-g)*3)+g*6
print(i)
        

import math
k=int(input())
ans=0
m_gcd=math.gcd
for h in range(1,k+1):
    for i in range(1,k+1):
        for j in range(1,k+1):
            ans+=m_gcd(m_gcd(h,i),j)
print(ans)


Verdicts: Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
from fractions import gcd

k = int(input())

res = 0
mul = [0, 1, 3, 6]
for a in range(1, k+1):
    for b in range(a, k+1):
        for c in range(b, k+1):
            res += gcd(gcd(a, b), c) * mul[len({a, b, c})]

print(res)

from math import gcd

k = int(input())

res = 0
mul = (0, 1, 3, 6)
for a in range(1, k+1):
    for b in range(a, k+1):
        for c in range(b, k+1):
            res += gcd(gcd(a, b), c) * mul[len({a, b, c})]

print(res)


Verdicts: Time Limit Exceeded

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
def gcd(x,y):
  while y>0:
    bk=x%y
    x=y
    y=bk
  return x

k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    for h in range(1,k+1):
      ans+=1
print(ans)

import math
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    tmp=math.gcd(i,j)
    for h in range(1,k+1):
      ans+=math.gcd(tmp,k)
print(ans)

import math
k=int(input())
ans=0
for i in range(1,k+1):
  for j in range(1,k+1):
    tmp=math.gcd(i,j)
    for h in range(1,k+1):
      ans+=math.gcd(tmp,h)
print(ans)

Verdicts: Wrong Answer

Wrong Answer

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import itertools
import math

m = int(input())
g = range(1, m+1)
res = 0
for c in itertools.combinations(g, 3):
  set_c = set(c)
  if len(set_c) == 3:
    n = 6
  elif len(set_c) == 2:
    n = 3
  else:
    n = 1
  tmp_res = math.gcd(c[0], c[1], c[2])
  res += tmp_res * n
print(res)

import itertools
import math

m = int(input())
g = list(range(1, m+1))
res = 0
for c in itertools.combinations_with_replacement(g, 3):
  set_c = set(c)
  set_list_c = list(set_c)
  if len(set_c) == 3:
    n = 6
    tmp_res = math.gcd(set_list_c[0], set_list_c[1])
    tmp_res = math.gcd(tmp_res, set_list_c[2])
  elif len(set_c) == 2:
    n = 3
    tmp_res = math.gcd(set_list_c[0], set_list_c[1])
  else:
    n = 1
    tmp_res = set_list_c[0]
  res += tmp_res * n
print(res)

Verdicts: Runtime Error

Accepted
Problem: Find \displaystyle{\sum_{a=1}^{K}\sum_{b=1}^{K}\sum_{c=1}^{K} \gcd(a,b,c)}.  Here \gcd(a,b,c) denotes the greatest common divisor of a, b, and c.

Submission attempts (in order):
import math
n=int(input())
add=0
for i in range(n):
    for j in range(n):
        for k in range(n):
            add+=math.gcd(math.gcd(i,j),k)
print(add)


import math
cnt=0
n=int(input())
for i in range(1,n+1):
    for j in range(1,n+1):
        wk=math.gcd(i,j)
        for k in range(1,n+1):
            cnt+=math.gcd(wk,k)
print(cnt)

Verdicts: Wrong Answer

Accepted