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 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

f = factorization(int(input()))
c=0
for _,i in f:
    if _ == 1:
        print(0)
        exit()

    a=int(2*i**0.5)

    if a*(a+1) <= i*2 <(a+1)*(a+2):
        c+=a
    elif i*2 >= a*(a+1):
        c+=a+1
    else:
        c+=a-1
print(c)

Submission status: Wrong Answer

Solution code:
n = int(input())
i = 2
count = 0

while True:
  if n % i == 0:
    #print("warikireru", i)
    n = n // i
    #print('n', n)
    count = count + 1
  if i > n:
    break
  i = i + 1

print(count)

Submission status: Wrong Answer

Solution code:
N = int(input())
ans = 0
for i in range(2, 10 ** 7 + 1):
    if N // i == N / i:
        ans += 1
        N = N // i

if N > 10 ** 7:
    ans += 1
print(ans)

Submission status: Wrong Answer

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

def make_divisors(n, cache):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0 and i not in cache:
            divisors.append(i)
            if i != n // i and n // i not in cache:
                divisors.append(n//i)

    divisors.sort()
    return divisors

def main():
    n = int(input())
    cache = set()
    i = 0
    while n > 1:
        a = make_divisors(n, cache)[1:]
        if len(a) == 0:
            break
        d = a[0]
        n //= d
        cache.add(d)
        i += 1

    print(i)





main()

Submission status: Wrong Answer

Solution code:
import math

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]

def main():
    N = int(input())
    divisors = make_divisors(N)[1:]
    cnt = 0
    while len(divisors) != 0:
        d = divisors.pop(0)
        e = 1
        # print(d,e)
        # print('===================')
        while N%d**e == 0:
            # print(d,N,e,cnt)
            N = N/(d**e)
            e += 1
            cnt += 1
        #     print(d,N,e,cnt)
        # print('===================')
    print(cnt)
    # A,B = [x for x in input().split()]
    # print(math.floor(int(A)*float(B)))

if __name__ == '__main__':
    main()

Submission status: Wrong Answer

Solution code:
#d
n = int(input())
import math
def is_prime(n):
    if n == 1: return False
    for k in range(2, int(math.sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
    

used = []
ans = 0
for i in range(2,int(math.sqrt(n)) + 1):
    if is_prime(i):
        if n%i ==0:
            n = n/i
            used.append(i)
            ans += 1    

    else:
        for j in used:
            k = j**2
            count = 2
            flag = 0

            while k <= i:
                k = j**count
                if k == i:
                    if n % i == 0:
                        n = n/i
                        ans += 1
                        flag = 1
                        break
                count+= 1
            if flag == 1:
                break
    if i > n:
        break
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())

def factorization(n):
    d = {}
    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
            d[i] = cnt

    if temp!=1:
        d[temp] = 1

    if d.keys()==[]:
        d[n] = 1

    return d

def get_a(n):
    if n==2:
        return [2]
    else:
        a = [1]
    while 1:
        n = n - a[-1]
        #print(n)
        if n<=0:
            break
        if n >= 0:
            a.append(a[-1]+1)
        else:
            a.append(n)
    return a

ans = 0
fact_dict = factorization(n)
#print(fact_dict)

for key, val in fact_dict.items():
    #print(key, val, get_a(val))
    ans += len(get_a(val))

if ans>0:
    print(ans)
else:
    print(0)

Submission status: Wrong Answer

Solution code:
a = int(input())

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
    
li = factorization(a)
ct = 0
for i,j in li:
    ct += (1 + j)//2
print(ct)

Submission status: Wrong Answer

Solution code:
def factorization(y):
    arr = []
    temp = y
    for i in range(2, int(-(-y**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([y, 1])
    return arr
import math
n=int(input())
if n==1:
  print(0)
  exit()

ans=0
l=factorization(n)
for i,j in l:
  cnt=0
  for k in range(2,int(math.sqrt(i))+1):
    if i%k==0:
      cnt=1
      break
  if cnt==0:
    if j<=2:
      ans+=1
    else:
      c=1
      t=1
      while j>0:
        ans+=1
        j-=c
        c+=t
        if j<t:
          break
        t+=1     
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())

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
if is_prime(n):
    print(1)
    exit()


cnt = 0
z = 2
while True:
    if n % z == 0:
        n = n //z
        cnt += 1
        z += 1
    else:
        z += 1
    #print("n.cnt",n,cnt)
    if n == 1 or is_prime(n) == True:
        print(cnt)
        exit()

Submission status: Wrong Answer

Solution code:
def seachPrimeNum(N):
    max = int(N ** (1/2))
    seachList = [i for i in range(2,N+1)]
    primeNum = []
    while seachList[0] <= max:
        primeNum.append(seachList[0])
        tmp = seachList[0]
        seachList = [i for i in seachList if i % tmp != 0]
    primeNum.extend(seachList)
    return primeNum

a = seachPrimeNum(10 ** 6)
n=(int)(input())
ans = 0
sumi = True
if n < 2:
  print(ans)
  sumi = False
else:
  ans = 0
  count = 0
  while(count < 78498):
    temp = 0
    while(n % a[count] == 0):
      n = n // a[count]
      temp += 1
    if temp >= 36:
      ans += 8
    elif temp >= 28:
      ans += 7
    elif temp >= 21:
      ans += 6
    elif temp >= 15:
      ans += 5
    elif temp >= 10:
      ans += 4
    elif temp >= 6:
      ans += 3
    elif temp >= 3:
      ans += 2
    elif temp >= 1:
      ans += 1
    
    count += 1
    temp = 0
    if n < 2:
      print(ans)
      sumi = False
      break
  if count == 78498 and sumi:
      print(1)
#print(a[78497:])

Submission status: Wrong Answer

Solution code:
N=int(input())
Nk=N
rootN=int(N**0.5)
p=[1]*(rootN+1)
p[0]=0
p[1]=0
for i in range(2,rootN+1):
    for j in range(i*2,rootN,i):
        p[j]=0
ps=[i for i in range(1,rootN) if p[i]==1]
pq=[]
for i in ps:
    c=0
    for j in range(1,41):
        if (N/i).is_integer():
            c+=1
            N/=i
        else:
            break
    if c!=0:
        pq.append(c)

res=0
for j in pq:
    c=0
    for k in range(1,41):
        if j-k >=0:
            c+=1
            j-=k
        else:
            break
    res+=c
if N > rootN:
    res*=2
if N==Nk:
    res+=1
    
print(res)

Submission status: Wrong Answer

Solution code:
import math
n = int(input())

def isPrime(n):
  if n == 2:
    return True
  if n % 2 == 0:
    return False
  
  # nの平方根まで計算する
  m = math.floor(math.sqrt(n)) + 1
  for p in range(3, m, 2):
      if n % p == 0:
        return False
  return True

if isPrime(n):
    print(1)
    exit()

ans = 0
for i in range(2,10**5):
    if n%i == 0:
        if n == 1:
            break
        n = n/i
        ans += 1
        

print(ans)

Submission status: Wrong Answer

Solution code:
#nの素数判定
def is_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

import bisect,collections,copy,heapq,itertools,math,string
import sys
def S(): return sys.stdin.readline().rstrip()
def M(): return map(int,sys.stdin.readline().rstrip().split())
def I(): return int(sys.stdin.readline().rstrip())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LS(): return list(sys.stdin.readline().rstrip().split())
n = I()
ans = 0
if n == 1:
    ans = 0
elif n == 2:
    ans = 1
elif is_prime(n):
    ans = 1
else:
    l = [i for i in range(2, 10000000)]
    for i in l:
        if n % i == 0:
            ans += 1
            n = n//i
        if n == 1:
            break
print(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 * 3
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
    for i in range(2, 100010):
        if is_prime[i]:
            if n % (i) == 0:
                ans += 1
                n = n // (i)

        if n == 1:
            break

    print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
a = {}
max_count = 0
while n % 2 == 0:
    if 2 in a:
        a[2] += 1
    else:
        a[2] = 1
#    a.append(2)
    n //= 2
    max_count += 1

f = 3
while f * f <= n:
    if n % f == 0:
        if f in a:
            a[f] += 1
        else:
            a[f] = 1
        n //= f
    else:
        f += 2

if n > 1:
    a[n] = 1

cnt = 0
for k, v in a.items():
    d = 1
    while (v - d >= 0):
        v = v - d
        d +=1
        cnt += 1

print(cnt)

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)

dividers = []

N_MAX = 10 ** 12

for p in u1000primes:
    for m in range(1, 50):
        dividers.append(p ** m)

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())


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

def count(m):
    count = 0
    for i in range(1, 10**12+1):
        if m >= i :
            m -= i
            count += 1
        else:
            return count


bun = factorization(n)

kazu = len(bun)

if kazu == 1 and bun[0][1] ==1:
    print(0)
    exit(0)


countup = 0
for i in range(kazu):
    countup += count(bun[i][1])

print(countup)

Submission status: Wrong Answer

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

if N == 1:
  print(0)
for i in range(2, N+1):
  if N%i== 0:
    N = N/i
    count +=1
  else:
    N = N
    
print(count)

Submission status: Wrong Answer

Solution code:
import math

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())

l = make_divisors(N)
ans = 1
count = -1

for i in range(len(l)):
    count += 1
    ans *= l[i]
    if ans >= N:
        print(count)
        exit()

Submission status: Wrong Answer

Solution code:
import math
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

a=int(input())
b=factorization(a)
ans=0
for i in range(len(b)):
    c=b[i][1]
    check=math.ceil(((-1)+math.sqrt(1+8*c))/2)
    ans=ans+check
if a==1:
    print(0)
else:
    print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())
cnt_list = [1,3,6,10,15,21,28,36]

def get_list(i):
    loop_cnt = int(-(-i**0.5//1))+1
    ret_list = []
    j = 2
    cnt = 0
    while j <= loop_cnt:
        if i % j == 0:
            i /= j
            cnt += 1
        else:
            if cnt > 0:
                for k in range(8):
                    if cnt < cnt_list[k]:
                        break
                for _ in range(k):
                    ret_list.append(j)
                cnt = 0
            j += 1
    if i != 1:
        ret_list.append(i)
    return ret_list

print(len(get_list(n)))

Submission status: Wrong Answer

Solution code:
import itertools

N = int(input())

# 素因数分解
# 戻り値: リスト
def prime_factor(n):
    ass = []
    for i in range(2,int(n**0.5)+1):
        while n % i==0:
            ass.append(i)
            n = n//i
    if n != 1:
        ass.append(n)
    return ass

pf = prime_factor(N)
if len(pf) == 0:
    print(0)
    exit()

d = {}
for i in pf:
    if i not in d:
        d[i] = 1
        continue
    d[i] += 1

exist_num = []
ans = 0
for k in d.keys():
    for c in range(1, 100):
        if d[k] >= c:
            exist_num.append(k ** c)
            ans += 1
            d[k] -= c

l = []
for k in d.keys():
    if d[k] > 0:
        for _ in range(d[k]):
            l.append(k)

for i in range(1, len(l)+1):
    combs = list(itertools.combinations(l, i))
    if len(combs) > 0:
        for comb in combs:
            n = 1
            for j in comb:
                n *= j
            if n not in exist_num and n != 1:
                ans += 1
                exist_num.append(n)
print(ans)

Submission status: Wrong Answer

Solution code:
n = int(input())

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


hoge = factorization(n)
ret = len(hoge)

if (hoge[0][0] == 1):
    print(0)
else:
    for i in hoge:
        cnt = i[1]
        sub = 1
        while cnt - sub >= 0:
            sub += 1
            cnt -= sub
        if i[1] != 1 and i[1] != 2:
            ret += sub - 1
    print(ret)

Submission status: Wrong Answer

Solution code:
# Contest No.: ABC169
# Problem No.: D
# Solver:      JEMINI
# Date:        20200531

import sys
import heapq

def main():
    temp = [True] * (10 ** 6 + 10)
    temp[0] = False
    temp[1] = False
    for i in range(2, 10 ** 6 + 10):
        if temp[i]:
            cnt = 2 * i
            while cnt < 10 ** 6 + 10:
                temp[cnt] = False
                cnt += i
    prime = []
    for i in range(10 ** 6 + 10):
        if temp[i]:
            prime.append(i)

    n = int(input())
    ans = 0
    tempN = n
    for i in prime:
        if i > n:
            break
        if tempN % i:
            continue
        div = 0
        while True:
            cnt = 1
            temp = 2
            while tempN % (i ** (div + 2 * temp)) == 0:
                cnt += 1
                temp *= 2
            if tempN % (i ** (div + cnt)):
                break
            div += cnt
        tempN = tempN // (i ** div)
        #print(div)
        if div > 2:
            div = int((div * 2) ** 0.5)
        else:
            div = 1
        #print(i, div, tempN)
        ans += div
    if tempN > 1:
        ans += 1
    print(ans)
    return

if __name__ == "__main__":
    main()

Submission status: Wrong Answer

Solution code:

import collections

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
c = collections.Counter(prime_factorize(int(input())))
# c = prime_factorize(int(input()))
a = 0
print(c)
for i in c.values():
    # print(i)
    x = 1
    while i > 0:
        i -= x
        a += 1
        x += 1
        print(i,x,a)
        if i < 0 :
            a -= 1

# a,z = 0,0
# for i in c:
#     if z == i :
#         z = 0
#     else :
#         z = i
#         a += 1
print(a)

Submission status: Wrong Answer

Solution code:
def prime_factorize(n):
    a = {}
    while n % 2 == 0:
        if 2 not in a:
            a[2] = 1
        else:
            a[2] += 1
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            if f not in a:
                a[f] = 1
            else:
                a[f] += 1
            n //= f
        else:
            f += 2
    if n != 1:
        if f not in a:
            a[f] = 1
        else:
            a[f] += 1
    return a

x = int(input())
y = prime_factorize(x)

num = 0
for v in y.values():
    now_v = v
    i = 1
    while True:
        # print(now_v)
        if now_v < i:
            break
        now_v -= i
        num += 1
        i += 1

print(num)

Submission status: Wrong Answer

Solution code:
import collections

N = int(input())

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

c = collections.Counter(prime_factorize(N))
print(c)

ans=0
for i in c.values():
    tmp = i
    cnt=0
    val=1
    while True:
        tmp = tmp-val
        val+=1

        if tmp > 0:
            cnt+=1
        
        if tmp == 0:
            cnt+=1
            ans+=cnt
            break
        
        if tmp < 0:
            ans+=cnt
            break

print(ans)

Submission status: Wrong Answer

Solution code:
import itertools
from collections import defaultdict

N = int(input())

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[i] = cnt

    if temp!=1:
        arr[temp] = 1

    if arr==[]:
        arr[n] = 1

    return arr

ng = {}
lv = 1
F = factorization(N)

f_candidate = []
result = 0
remain = 0
for k, v in F.items():
    remain += v

while remain > 0:

    # 候補を取得
    for k, v in F.items():
        for i in range(max(lv, v)):
            f_candidate.append(k)

    candidates = itertools.combinations_with_replacement(f_candidate, lv)
    allNg = True
    for candidate in candidates:
        red_map = defaultdict(int)

        next = False
        value = 1

        for c in candidate:
            value *= c
            red_map[c] += 1
            if red_map[c] > F[c]:
                next = True
                break
        if next:
            continue

        if value in ng:
            continue

        ng[value] = True
        result+=1

        # 減らす
        for c in candidate:
            F[c] -= 1
            remain -= 1
        allNg = False
        break

    if allNg:
        lv+=1
    if lv > remain:
        break

print(result)

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

fact = factorization(997764507000)

count = 0

for tup in fact:
    countTup = 0
    while True:
        countTup += 1
        if tup[1] < countTup:
            break
        tup[1] -= countTup
    count += countTup - 1
    
print(count)

Submission status: Wrong Answer

Solution code:
import math
from collections import defaultdict


N = int(input())
n = N
#素因数分解
factor = defaultdict(lambda: 0)
tmp = int(math.sqrt(N))+1
for num in range(2,tmp):
    while N % num == 0:
        N //= num
        factor[num] += 1
if not factor:
    factor[n] += 1
elif N != 1:
    factor[N] += 1



ans = 0
for num in factor:
    i = 1
    while True:
        factor[num] -= i
        if factor[num]<0:
            break
        ans += 1
        i+=1

print(ans)

Submission status: Wrong Answer

Solution code:
n= int(input())

def div(x):
	for p in primes:
		if p>x**0.5:
			break
		if x%p== 0:
			return False
	return True

primes= [2]
for num in range(3, int(n**0.5)):
	if div(num):
		primes.append(num)

###

prime_factors= {}

while n != 1:
	for p in primes:
		if n%p==0:
			if p in prime_factors:
				prime_factors[p]+=1
				n= int(n/p)
				break
			else:
				prime_factors[p]=1
				n= int(n/p)
				break
		elif div(n):
			if n in prime_factors:
				prime_factors[n]+=1
				n=1
				break
			else:
				prime_factors[n]=1
				n=1
				break
tot= 0
for p in prime_factors:
	if prime_factors[p]>=36:
		tot+= 8
	elif prime_factors[p]>=28:
		tot+=7
	elif prime_factors[p]>=21:
		tot+=6
	elif prime_factors[p]>=15:
		tot+=5
	elif prime_factors[p]>=10:
		tot+=4
	elif prime_factors[p]>=6:
		tot+=3
	elif prime_factors[p]>=3:
		tot+=2
	else:
		tot+=1
print(prime_factors)		
print(tot)