Problem:


Score : 400 points

Problem Statement

Given is a positive integer N. Consider repeatedly applying the operation below on N:

First, choose a positive integer z satisfying all of the conditions below:

z can be represented as z=p^e, where p is a prime number and e is a positive integer;

z divides N;

z is different from all integers chosen in previous operations.

Then, replace N with N/z.

Find the maximum number of times the operation can be applied.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the maximum number of times the operation can be applied.

Sample Input 1

24

Sample Output 1

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=12.)

Choose z=3 (=3^1). (Now we have N=4.)

Choose z=4 (=2^2). (Now we have N=1.)

Sample Input 2

1

Sample Output 2

0

We cannot apply the operation at all.

Sample Input 3

64

Sample Output 3

3

We can apply the operation three times by, for example, making the following choices:

Choose z=2 (=2^1). (Now we have N=32.)

Choose z=4 (=2^2). (Now we have N=8.)

Choose z=8 (=2^3). (Now we have N=1.)

Sample Input 4

1000000007

Sample Output 4

1

We can apply the operation once by, for example, making the following choice:

z=1000000007 (=1000000007^1). (Now we have N=1.)

Sample Input 5

997764507000

Sample Output 5

7



Sample input:
24


Sample output:
3

Submission status: Wrong Answer

Solution code:
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

A = prime_factorize(int(input()))
B = []

for a in set(A):
  if A.count(a)==1:
    pass
  else:
    n = 1
    while 0.5*n*(n+1)<+A.count(a):
      n+=1
    
    if n>1:
      B.append(n-1)
    
print(len(set(A))+sum(B))

Submission status: Wrong Answer

Solution code:
import math
N = int(input())
L = N
if L == 1:
    print(0)
else:
    num = 0
    if L > 100000000:
        limit = int(math.sqrt(L)) + 2
    else:
        limit = L
    for i in range(2, limit):
        if N % i == 0:
            N = N / i
            num = num + 1

    if num == 0:
        print(1)
    else:
        print(num)

Submission status: Wrong Answer

Solution code:
"""
N = list(map(int,input().split()))
S = [str(input()) for _ in range(N)]
S = [list(map(int,list(input()))) for _ in range(h)] 
print(*S,sep="")
"""

import sys
sys.setrecursionlimit(10**6)
input = lambda: sys.stdin.readline().rstrip()
inf = float("inf") # 無限
# 参考URL
# https://qiita.com/LorseKudos/items/9eb560494862c8b4eb56
def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

n = int(input())

divisor_list = make_divisors(n)
divisor_list.remove(1)

count = 0

# print(divisor_list)

for divisor in divisor_list[:]:
    # print("n:{} div:{}".format(n,divisor))
    if n%divisor==0:
        count += 1
        n = int(n/divisor)
print(count)

Submission status: Wrong Answer

Solution code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr
ans = 0
n = int(input())
f = [None for _ in range(40)]
f[1] = 1
for i in range(2, 40):
    if (f[i-1]+1)*(f[i-1]+2) == 2*i:
        f[i] = f[i-1]+1
    else:
        f[i] = f[i-1]

if n==1:
    print(0)
else:
    arr = factorization(n)
    for a,b in arr:
        ans += f[b]
print(ans)

Submission status: Wrong Answer

Solution code:
import math
p =0 
def prime_factorize(n):
    a = []
    b = []
    k = 0
    while n % 2 == 0:
        a.append(2)
        n //= 2
        k += 1
    f = 3
    f_prev = 2
    if k !=0 :
      b.append(k)
    k = 0
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
            k += 1
            if f != f_prev:
              b.append(k)
            f_prev = f
        else:
            f_prev = f
            k = 0
            f += 2
    if n != 1:
        a.append(n)
        b.append(1)
    return b
  
n = int(input())
b2 = prime_factorize(n)
m = len(b2)
for l in range(m):
  p += math.floor((1+(1+8*b2[l])**0.5/2)) -1


print(p)

Submission status: Wrong Answer

Solution code:
n = int(input())
ans = 0

#########################  ネットから拾ってきた
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a
######################### 

soinnsuu = prime_factorize(n)

import collections
c = collections.Counter(soinnsuu)

z = []
amari = []

for i in sorted(set(soinnsuu)):
    res = c[i]
    for j in range(1,50):
        res -= j
        
        if res >= 0:
            ans += 1
            z.append(i**j)
            
        else:
            for k in range(-1*res):
                amari.append(i)
                
            break
                
                
                
import itertools
hosei = []
 
for i in range(len(amari)):
    c = list(itertools.combinations(amari,i+1))
    
    for j in c:
        add = 1
        
        for k in range(i+1):
            add *= j[k]
            
        if add not in z:
            hosei.append(add)
            
for i in z:
    n //= i
        
for i in hosei:
    if n % i == 0:
        n //= i
        ans += 1
        
    if n == 1:
        break
        
print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
A = []
import math
n = int(math.sqrt(N))+1
for i in range(2,n):
  a = 0
  while N % i == 0:
    N = N//i
    a += 1
  j = 1
  while a-j>=0:
    A.append(j)
    a = a-j
    j += 1
ans = len(A)
if ans == 0 and N != 1:
  ans = 1
print(ans)

Submission status: Wrong Answer

Solution code:
import math

N = int(input())

z = []

def isprime(n):
    if n <= 1:
        return False
    for i in range(2, int(math.sqrt(n)) + 1):
        if n % i == 0:
            return False
    return True

def judge(n):
    if isprime(n):
        return True
    for i in range(2, int(math.sqrt(n)+1)):
        if n % i == 0:
            n = n // i
            while n != 1:
                if n % i != 0:
                    return False
                n //= i
            return True
        return False


ans = 0
num = []
i = 2
while N != 1:
    
    if isprime(N):
        ans += 1
        break
    if N % i == 0 and judge(i): 
        N //= i
        ans += 1
        num.append(i)

    i += 1
    



print(ans)

Submission status: Wrong Answer

Solution code:
from collections import Counter

def Eratosthenes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n ** 0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]

n = int(input())
n2 = n

if n < 2:
    print(0)
    exit()

prime_factors = [] #素因数
for i in Eratosthenes(int(n ** 0.5)):
    if i**2 > n2:
        break
    while n2 % i == 0:
        prime_factors.append(i)
        n2 //= i
if n2 > 1:
    prime_factors.append(n2)

ans = []
list = []
for i in prime_factors:
    if i in list:
        tmp = list.pop(list.index(i)) * i
        ans.append(tmp)
    elif i in ans:
        list.append(i)
    else:
        ans.append(i)

print(len(ans))

Submission status: Wrong Answer

Solution code:
n = int(input())
def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return factors
f = list(set(prime_factors(n)))
print(f)
ans = 0
for i in f:
    e = 1
    while n % i**e == 0:
        n = n//(i**e)
        ans += 1
        e+=1

print(ans)

Submission status: Wrong Answer

Solution code:
import numpy as np

def seachPrimeNum2(N):
    max = int(np.sqrt(N))
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    primeNum2 = []
    while seachList[0] <= max:
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    for i in range(1,10):
      for j in primeNum:
        primeNum2.append(j**i)
    return primeNum2
def seachPrimeNum3(N):
    max = int(np.sqrt(N))
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    primeNum2 = []
    while seachList[0] <= max:
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    for i in range(1,6):
      for j in primeNum:
        primeNum2.append(j**i)
    return primeNum2
def seachPrimeNum4(N):
    max = int(np.sqrt(N))
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    primeNum2 = []
    while seachList[0] <= max:
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    for i in range(1,3):
      for j in primeNum:
        primeNum2.append(j**i)
    return primeNum2
P = seachPrimeNum2(10000)
P += seachPrimeNum3(100000)
P = set(P+seachPrimeNum4(1000000))
N = int(input())
ans = 0
for p in P:
  if N%p == 0:
    ans += 1
    N = N//p
print(max(1,ans))

Submission status: Wrong Answer

Solution code:
#デフォルト
import itertools
from collections import defaultdict
import collections
from decimal import *
import math
import sys
sys.setrecursionlimit(200000)
mod = 1000000007

n = int(input())

def Prime(n):
    if n == 1:
        return False
    for i in range(2,int(n**0.5)+1):
        if n % i == 0:
            return False
    return True

MAX = 100010 * 5
is_prime = [False] * MAX
is_prime[0] = False
is_prime[1] = False
for i in range(2, MAX):
    if Prime(i):
        j = i * i
        is_prime[i] = True
        while j < MAX:
            is_prime[j] = True
            j *= i
if (Prime(n)):
    print("1")
else:
    ans = 0
    ss = n
    for i in range(2, MAX):
        if is_prime[i]:
            if ss % i == 0:
                ans += 1
                ss = ss / i

        if ss == 1:
            break
    ans2 = 0
    for i in reversed(range(2, MAX)):
        if is_prime[i]:
            if n % i == 0:
                ans2 += 1
                n = n / i

        if n == 1:
            break
    print(max(ans,ans2))

Submission status: Wrong Answer

Solution code:
import sys
import math
input = sys.stdin.readline

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

def solve(n):
    factors = {} 
    if n % 2 == 0:
        factors[2] = 0
        while n % 2 == 0: 
            factors[2] += 1 
            n = n / 2
          
    # n must be odd at this point 
    # so a skip of 2 ( i = i + 2) can be used 
    for i in range(3,int(math.sqrt(n))+1,2): 
          
        # while i divides n , print i ad divide n 
        while n % i== 0: 
            if i in factors:
                factors[i] += 1
            else: factors[i] = 1
            n = n / i 
              
    # Condition if n is a prime 
    # number greater than 2 
    if n > 2: 
        factors[n] = 1	
    return factors 

def main():
    n = inp()
    answer = solve(n)
    print(answer)
    set1 = []
    res = 0 
    for key,value in answer.items():
        res -= 1
        d = 1
        while value >= d:
            value -=d
            d += 1
        res +=d

    print(res)

main()

Submission status: Wrong Answer

Solution code:
# -*- coding: utf-8 -*-

# 入力を整数に変換して受け取る
def input_int():
    return int(input())


# マイナス1した値を返却
def int1(x):
    return int(x) - 1


# 半角スペース区切り入力をIntに変換してMapで受け取る
def input_to_int_map():
    return map(int, input().split())


# 半角スペース区切り入力をIntに変換して受け取る
def input_to_int_tuple():
    return tuple(map(int, input().split()))


# 半角スペース区切り入力をIntに変換してマイナス1した値を受け取る
def input_to_int_tuple_minus1():
    return tuple(map(int1, input().split()))

import math

def factorization(n):
    # 素因数を格納するリスト
    factor = []
    # 2から√n以下の数字で割っていく
    tmp = int(math.sqrt(n)) + 1
    target = n
    for num in range(2, tmp):
        while target % num == 0:
            target //= num
            factor.append(num)

    # リストが空ならそれは素数
    if not factor and n != 1:
        factor.append(n)

    return factor


def main():
    n = input_int()

    a = factorization(n)

    target = set()

    from collections import deque
    tyofuku = []

    for _a in a:
        if _a in target:
            tyofuku.append(_a)
        else:
            target.add(_a)

    mult = 1
    for i in tyofuku:
        mult *= i

    for i in range(2, mult + 1):
        if i not in target and mult % i == 0:
            target.add(i)
            mult /= i

    print(len(target))


if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
import math
n = int(input())
def makeprime(value):
    flag  = [True for _ in range(value)]
    ans = []
    for i in range(1,len(flag)):
        if flag[i]:
            ans.append(i+1)
            for j in range(i,len(flag),i+1):
                flag[j] = False
    return ans
for i in range(2,int(math.sqrt(n)+1)):
    if n%i == 0:
        flag = 1
        break
else:
    flag = 0
if flag:
    r = n
    ans = 0
    rem = makeprime(int(math.sqrt(n)))
    for i in rem:
        o = 1
        while (i**o <= n):
            if n%i**o == 0:
                ans += 1
                n //= i**o
            o += 1
    print(ans)
else:
    if n == 1:
        print(0)
    else:
        print(1)

Submission status: Wrong Answer

Solution code:

def pri_me(x):
    if x == 2:
        return True
    for i in range(2,int(x**0.5)+1):
        if x%i==0:
            return False
    return True
#print(pri_me(n))


def prime_factorize(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a

n = int(input())
if n==1 or n == 0:
    print(0)
    exit()
if pri_me(n):
    print(1)
    exit()
N = n
ans = 0
for i in range(2,N+1):
    if n%i==0: 
        n=n//i
        ans += 1
        if n <=i:
            break
        #print(n,i)
        #print(len(set(prime_factorize(i)))
print(ans)

Submission status: Wrong Answer

Solution code:
from decimal import *
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr
n = int(input())
li = []
for i in factorization(n):
    ran = range(i[1]+1)
    sum = 0
    s = 0
    ss = 1
    for j in ran:
        sum += 1
        if sum > s:
            li.append(i[0]**(j))
            s = ss + s
            ss += 1
ans = 1
count = 0
for i in sorted(set(li)):
    ans = int(Decimal(str(ans)) * Decimal(str(i)))
    count += 1
    if ans == n:
        break
print(count-1)

Submission status: Wrong Answer

Solution code:
n = int(input())


def prime_factorize_n(n):
    a = []
    while n % 2 == 0:
        a.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        a.append(n)
    return a


a_list = prime_factorize_n(n)
# print(a_list)

tmp = 1
used_list = []
for i in range(len(a_list)):
    if a_list[i] not in used_list:
        used_list.append(a_list[i])

    else:
        if tmp == 1:
            tmp = a_list[i]

        else:
            if tmp % a_list[i] == 0:
                tmp *= a_list[i]
                if tmp not in a_list:
                    used_list.append(tmp)
                    tmp = 1
            else:
                tmp = 1

# print(used_list)
print(len(used_list))

Submission status: Wrong Answer

Solution code:
def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr

import math

def kaisa(x):
  first = math.floor(math.sqrt(x*2))
  if x*2 >= first*(first+1):
    return first
  else:
    return first-1

n = int(input())
soinsu = factorization(n) 

res = 0
for i in soinsu:
  res = res + kaisa(i[1])
print(res)

Submission status: Wrong Answer

Solution code:
import math
from sys import exit

n=int(input())
primes = {}
i = 2
ans = 0
square = math.floor(math.sqrt(n))

if n == 1:
    print(0)
    exit()

while True:
    if n == 1 or i > square:
        break
    if n % i == 0:
        if i not in primes.keys():
            primes[i] = 1
        else:
            primes[i] += 1
        n = n // i
    else:
        if i == 2:
            i += 1
        else:
            i += 2
        continue

if len(primes) == 0:
    print(1)
    exit()

for k,v in primes.items():
    if k == 1:
        continue
    base = v * 2
    root = math.floor(math.sqrt(base))
    if root * (root + 1) > base:
        root -= 1
    ans += root

print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
ans = 0

def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

A = make_divisors(n)

for i in range(1, len(A)):
    if n % A[i] == 0:
        n = n // A[i]
        ans = ans + 1
    elif n < A[i]:
        break

print(ans)

Submission status: Wrong Answer

Solution code:
s = [input() for i in range(1)]
print(s)

Submission status: Wrong Answer

Solution code:
#n, m, q = map(int, input().split())
#List = list(map(int, input().split()))
#req = [list(map(int, input().split())) for _ in range(q)]
#t = t[:-1]
#print(ans[j], end = "") 改行無しで出力
#[0]*n
import collections
def divisor(n):
    i = 1
    table = []
    while i * i <= n:
        if n%i == 0:
            table.append(i)
            table.append(n//i)
        i += 1
    table = list(set(table))
    return table

n = int(input())
ans = 0

list = divisor(n)
sort = sorted(list)
del sort[0]

for i in range(len(sort)):
    if n % sort[i] == 0 and n > 1:
        n = n / sort[i]
        #print(n)
        ans += 1


print(ans)
#print(sort)

Submission status: Wrong Answer

Solution code:
"""
N = list(map(int,input().split()))
S = [str(input()) for _ in range(N)]
S = [list(map(int,list(input()))) for _ in range(h)] 
print(*S,sep="")
"""

import sys
sys.setrecursionlimit(10**6)
input = lambda: sys.stdin.readline().rstrip()
inf = float("inf") # 無限
# 参考URL
# https://qiita.com/LorseKudos/items/9eb560494862c8b4eb56
def make_divisors(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]

n = int(input())

divisor_list = make_divisors(n)
divisor_list.remove(1)

count = 0

# print(divisor_list)

for divisor in divisor_list[:]:
    # print("n:{} div:{}".format(n,divisor))
    if n%divisor==0:
        count += 1
        n //= divisor
print(count)

Submission status: Wrong Answer

Solution code:
import math
n = int(input())
ans = 0
k = int(math.sqrt(n)) + 2
for i in range(2,k):
    if n%i==0:
        ans+=1
        n = n//i
    if n==1:
        break
if ans==0:
    print(1)
else:
    print(ans)

Submission status: Wrong Answer

Solution code:
N = int(input())
current_num = 2
count = 0

import math
S=int(math.sqrt(N))
list1=[N]
while (S >= current_num):
  if N%current_num==0 :
    
    N=int(N/current_num)
    if N!=current_num :
      list1.append(N)
    count+=1
  current_num += 1


def p_judge(num) :
  q=int(math.sqrt(num))
  if num==1 :
    return False
  for i in range(2,q) :
    if num%i==0 :
      return False
  return True
list1=reversed(list1)
for item in list1 :
  if p_judge(item) and N%item==0 :
    N=int(N/item)
    count+=1

print(count)

Submission status: Wrong Answer

Solution code:
N = int(input())
ar =  set()

def is_prime(q):
    q = abs(q)
    if q == 2: return True
    if q < 2 or q&1 == 0: return False
    return pow(2, q-1, q) == 1

while N != 1:
    if is_prime(N):
        ar.add(N)
        break
    for i in range(2,N//2+1):
        if N%i == 0 and not i in ar:
            ar.add(i)
            break
    N = N//i
print(len(ar))

Submission status: Wrong Answer

Solution code:
from numba import jit
import math


@jit
def solve(N):
    cnt = 0
    for i in range(2, math.sqrt(N) + 1):
        if N % i == 0:
            N = N // i
            cnt += 1
        else:
            continue
    return cnt


@jit
def is_prime(N):
    for i in range(2, math.sqrt(N)):
        if N % i == 0:
            return False
        else:
            continue
    return True


def main():
    N = int(input())

    if N == 1:
        print(0)
        return
    if is_prime(N):
        print(1)
        return

    print(solve(N))


if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:
N = int(input())


# u1000primes = (
# 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
# 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
# 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
# 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
# 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
# 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
# 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031,
# 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171,
# 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303,
# 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471,
# 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607,
# 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753,
# 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913,
# 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081,
# 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239,
# 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381,
# 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549,
# 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699,
# 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843,
# 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019,
# 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203,
# 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359,
# 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529,
# 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673,
# 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847,
# 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007,
# 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159,
# 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339,
# 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517,
# 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679,
# 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877,
# 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021,
# 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209,
# 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407,
# 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557,
# 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717,
# 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869,
# 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079,
# 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257,
# 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389,
# 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599,
# 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781,
# 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959,
# 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127,
# 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321,
# 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523,
# 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673,
# 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867,
# 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059,
# 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233,
# 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423,
# 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623,
# 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761,
# 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951,
# 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137,
# 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319,
# 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467,
# 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661,
# 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833,
# 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973)

def primes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, int(n ** 0.5) + 1):
        if not is_prime[i]:
            continue
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i]]


prime_numbers = primes(1000000)

dividers = []

N_MAX = 10 ** 12

for p in prime_numbers:
    for m in range(1, 40):
        if p ** m <= N_MAX:
            dividers.append(p ** m)
        else:
            break


dividers = sorted([d for d in list(set(dividers)) if d <= N_MAX])


def isprime(n):
    '''check if integer n is a prime'''

    # make sure n is a positive integer
    n = abs(int(n))

    # 0 and 1 are not primes
    if n < 2:
        return False

    # 2 is the only even prime number
    if n == 2:
        return True

    # all other even numbers are not primes
    if not n & 1:
        return False

    # range starts with 3 and only needs to go up
    # the square root of n for all odd numbers
    for x in range(3, int(n ** 0.5) + 1, 2):
        if n % x == 0:
            return False

    return True


e_MAX = 50

used_numbers = []

if N == 1:
    used_numbers = []
elif isprime(N):
    used_numbers.append(N)
else:
    idx = 0
    while idx < len(dividers):
        z = dividers[idx]

        if z > N:
            break

        if N % z == 0 and z not in used_numbers:
            N = int(N / z)
            used_numbers.append(z)

            # print('div success:' + str(z))
            # print(N)

            if N == 1:
                break
        else:
            pass
            # print('div failed:' + str(z))

        idx += 1

# print(used_numbers)
print(len(used_numbers))

Submission status: Wrong Answer

Solution code:
N = int(input())

pf={}
m=N
ans = 0
for i in range(2,int(m**0.5)+1):
    while m%i==0:
        pf[i]=pf.get(i,0)+1
        m/=i
    sum = 1
    k = 1
    while pf.get(i,0)>=sum:
      k = k + 1
      sum = sum + k
    ans = ans+k-1
    #print(ans)
if m>1:
  pf[m]=1
  ans = 1
print(ans)