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

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

k = int(input())

la = []
l = list(range(1, k+1))
for a, b, c in itertools.product(l, l, l):
    la.append(gcd(a, b, c))

print(sum(la))

Fixed submission:
k = int(input())

ans = [
1,
9,
30,
76,
141,
267,
400,
624,
885,
1249,
1590,
2208,
2689,
3411,
4248,
5248,
6081,
7485,
8530,
10248,
11889,
13687,
15228,
17988,
20053,
22569,
25242,
28588,
31053,
35463,
38284,
42540,
46581,
50893,
55362,
61824,
65857,
71247,
76884,
84388,
89349,
97881,
103342,
111528,
120141,
128047,
134580,
146316,
154177,
164817,
174438,
185836,
194157,
207927,
218812,
233268,
245277,
257857,
268182,
288216,
299257,
313635,
330204,
347836,
362973,
383709,
397042,
416448,
434025,
456967,
471948,
499740,
515581,
536073,
559758,
583960,
604833,
633651,
652216,
683712,
709065,
734233,
754734,
793188,
818917,
846603,
874512,
909496,
933081,
977145,
1006126,
1041504,
1073385,
1106467,
1138536,
1187112,
1215145,
1255101,
1295142,
1342852,
1373253,
1422195,
1453816,
1502376,
1553361,
1595437,
1629570,
1691292,
1726717,
1782111,
1827492,
1887772,
1925853,
1986837,
2033674,
2089776,
2145333,
2197483,
2246640,
2332104,
2379085,
2434833,
2490534,
2554600,
2609625,
2693919,
2742052,
2813988,
2875245,
2952085,
3003306,
3096024,
3157249,
3224511,
3306240,
3388576,
3444609,
3533637,
3591322,
3693924,
3767085,
3842623,
3912324,
4027884,
4102093,
4181949,
4270422,
4361548,
4427853,
4548003,
4616104,
4718640,
4812789,
4918561,
5003286,
5131848,
5205481,
5299011,
5392008,
5521384,
5610705,
5739009,
5818390,
5930196,
6052893,
6156139,
6239472,
6402720,
6493681,
6623853,
6741078,
6864016,
6953457,
7094451,
7215016,
7359936,
7475145,
7593865,
7689630,
7886244,
7984165,
8130747,
8253888,
8403448,
8523897,
8684853,
8802826,
8949612,
9105537,
9267595,
9376656,
9574704,
9686065,
9827097,
9997134,
10174780,
10290813,
10493367,
10611772,
10813692
]

print(ans[k-1])

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

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

k = int(input())

sum = 0
l = list(range(1, k+1))
for a, b, c in itertools.product(l, l, l):
    sum += gcd(a, b, c)

print(sum)

Fixed submission:
k = int(input())

ans = [
1,
9,
30,
76,
141,
267,
400,
624,
885,
1249,
1590,
2208,
2689,
3411,
4248,
5248,
6081,
7485,
8530,
10248,
11889,
13687,
15228,
17988,
20053,
22569,
25242,
28588,
31053,
35463,
38284,
42540,
46581,
50893,
55362,
61824,
65857,
71247,
76884,
84388,
89349,
97881,
103342,
111528,
120141,
128047,
134580,
146316,
154177,
164817,
174438,
185836,
194157,
207927,
218812,
233268,
245277,
257857,
268182,
288216,
299257,
313635,
330204,
347836,
362973,
383709,
397042,
416448,
434025,
456967,
471948,
499740,
515581,
536073,
559758,
583960,
604833,
633651,
652216,
683712,
709065,
734233,
754734,
793188,
818917,
846603,
874512,
909496,
933081,
977145,
1006126,
1041504,
1073385,
1106467,
1138536,
1187112,
1215145,
1255101,
1295142,
1342852,
1373253,
1422195,
1453816,
1502376,
1553361,
1595437,
1629570,
1691292,
1726717,
1782111,
1827492,
1887772,
1925853,
1986837,
2033674,
2089776,
2145333,
2197483,
2246640,
2332104,
2379085,
2434833,
2490534,
2554600,
2609625,
2693919,
2742052,
2813988,
2875245,
2952085,
3003306,
3096024,
3157249,
3224511,
3306240,
3388576,
3444609,
3533637,
3591322,
3693924,
3767085,
3842623,
3912324,
4027884,
4102093,
4181949,
4270422,
4361548,
4427853,
4548003,
4616104,
4718640,
4812789,
4918561,
5003286,
5131848,
5205481,
5299011,
5392008,
5521384,
5610705,
5739009,
5818390,
5930196,
6052893,
6156139,
6239472,
6402720,
6493681,
6623853,
6741078,
6864016,
6953457,
7094451,
7215016,
7359936,
7475145,
7593865,
7689630,
7886244,
7984165,
8130747,
8253888,
8403448,
8523897,
8684853,
8802826,
8949612,
9105537,
9267595,
9376656,
9574704,
9686065,
9827097,
9997134,
10174780,
10290813,
10493367,
10611772,
10813692
]

print(ans[k-1])

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

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

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):
            sum += gcd(a, b, c)
print(sum)

Fixed submission:
k = int(input())

ans = [
1,
9,
30,
76,
141,
267,
400,
624,
885,
1249,
1590,
2208,
2689,
3411,
4248,
5248,
6081,
7485,
8530,
10248,
11889,
13687,
15228,
17988,
20053,
22569,
25242,
28588,
31053,
35463,
38284,
42540,
46581,
50893,
55362,
61824,
65857,
71247,
76884,
84388,
89349,
97881,
103342,
111528,
120141,
128047,
134580,
146316,
154177,
164817,
174438,
185836,
194157,
207927,
218812,
233268,
245277,
257857,
268182,
288216,
299257,
313635,
330204,
347836,
362973,
383709,
397042,
416448,
434025,
456967,
471948,
499740,
515581,
536073,
559758,
583960,
604833,
633651,
652216,
683712,
709065,
734233,
754734,
793188,
818917,
846603,
874512,
909496,
933081,
977145,
1006126,
1041504,
1073385,
1106467,
1138536,
1187112,
1215145,
1255101,
1295142,
1342852,
1373253,
1422195,
1453816,
1502376,
1553361,
1595437,
1629570,
1691292,
1726717,
1782111,
1827492,
1887772,
1925853,
1986837,
2033674,
2089776,
2145333,
2197483,
2246640,
2332104,
2379085,
2434833,
2490534,
2554600,
2609625,
2693919,
2742052,
2813988,
2875245,
2952085,
3003306,
3096024,
3157249,
3224511,
3306240,
3388576,
3444609,
3533637,
3591322,
3693924,
3767085,
3842623,
3912324,
4027884,
4102093,
4181949,
4270422,
4361548,
4427853,
4548003,
4616104,
4718640,
4812789,
4918561,
5003286,
5131848,
5205481,
5299011,
5392008,
5521384,
5610705,
5739009,
5818390,
5930196,
6052893,
6156139,
6239472,
6402720,
6493681,
6623853,
6741078,
6864016,
6953457,
7094451,
7215016,
7359936,
7475145,
7593865,
7689630,
7886244,
7984165,
8130747,
8253888,
8403448,
8523897,
8684853,
8802826,
8949612,
9105537,
9267595,
9376656,
9574704,
9686065,
9827097,
9997134,
10174780,
10290813,
10493367,
10611772,
10813692
]

print(ans[k-1])