Buggy python submission (verdict: Runtime Error):
#どっちで出すか注意, rstrip注意
#提出前に見返すこと！
def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10000000)
    from collections import Counter, deque
    #from collections import defaultdict
    from itertools import combinations, permutations, accumulate
    #from itertools import product
    from bisect import bisect_left,bisect_right
    import heapq
    from math import floor, ceil
    #from operator import itemgetter

    #inf = 10**17
    #mod = 10**9 + 7

    a,b = map(int, input().split())
    def yakusuu(a,b):
        n = int(a**.5)+1
        res1 = []
        res2 = []
        for i in range(1, n):
            if a%i==0:
                if b%i==0:
                    res1.append(i)
                elif b%(a//i)==0:
                    res1.append(a//i)
        return res1
    
    if a>b:
        a,b = b,a
    l = yakusuu(a,b)
    
    def primecheck(n):
        #0~nまで素数判定
        p = [True] * (n + 1)
        p[0] = False
        p[1] = False
        for i in range(2, int(n ** 0.5) + 1):
            if p[i]:
                for j in range(i * i, n + 1, i):
                    p[j] = False
        return p
    
    p = primecheck(max(l))
    res = 0
    for i in l:
        if p[i]:
            res += 1
    print(res+1)

if __name__ == '__main__':
    main()

Fixed submission:
#どっちで出すか注意, rstrip注意
#提出前に見返すこと！
def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10000000)
    from collections import Counter, deque
    #from collections import defaultdict
    from itertools import combinations, permutations, accumulate
    #from itertools import product
    from bisect import bisect_left,bisect_right
    import heapq
    from math import floor, ceil
    #from operator import itemgetter

    #inf = 10**17
    #mod = 10**9 + 7

    a,b = map(int, input().split())
    # 素因数分解
    def prime_decomp(n):
        i = 2
        res = []
        while i ** 2 <= n:
            while n % i==0:
                n //= i
                res.append(i)
            i += 1
        if n > 1:
            res.append(n)
        return res

    c = set(prime_decomp(a))
    d = set(prime_decomp(b))
    print(len(c&d)+1)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#どっちで出すか注意, rstrip注意
#提出前に見返すこと！
def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10000000)
    from collections import Counter, deque
    #from collections import defaultdict
    from itertools import combinations, permutations, accumulate
    #from itertools import product
    from bisect import bisect_left,bisect_right
    import heapq
    from math import floor, ceil
    #from operator import itemgetter

    #inf = 10**17
    #mod = 10**9 + 7

    a,b = map(int, input().split())
    def yakusuu(N):
        n = int(N**.5)+1
        res1 = []
        res2 = []
        for i in range(1, n):
            if N%i==0:
                res1.append(i)
                if N!=i**2:
                    res2.append(N//i)
        res2.reverse()
        return res1+res2
    
    if a>b:
        a,b = b,a
    l = yakusuu(a)
    yaku = []
    for i in l:
        if b%i == 0:
            yaku.append(i)
    
    def primecheck(n):
        #0~nまで素数判定
        p = [True] * (n + 1)
        p[0] = False
        p[1] = False
        for i in range(2, int(n ** 0.5) + 1):
            if p[i]:
                for j in range(i * i, n + 1, i):
                    p[j] = False
        return p
    
    p = primecheck(a)
    res = 0
    for i in yaku:
        if p[i]:
            res += 1
    print(res+1)

if __name__ == '__main__':
    main()

Fixed submission:
#どっちで出すか注意, rstrip注意
#提出前に見返すこと！
def main():
    import sys
    input = sys.stdin.readline
    sys.setrecursionlimit(10000000)
    from collections import Counter, deque
    #from collections import defaultdict
    from itertools import combinations, permutations, accumulate
    #from itertools import product
    from bisect import bisect_left,bisect_right
    import heapq
    from math import floor, ceil
    #from operator import itemgetter

    #inf = 10**17
    #mod = 10**9 + 7

    a,b = map(int, input().split())
    # 素因数分解
    def prime_decomp(n):
        i = 2
        res = []
        while i ** 2 <= n:
            while n % i==0:
                n //= i
                res.append(i)
            i += 1
        if n > 1:
            res.append(n)
        return res

    c = set(prime_decomp(a))
    d = set(prime_decomp(b))
    print(len(c&d)+1)


if __name__ == '__main__':
    main()