Problem:
 Score : 300 points    Problem Statement You are given an integer N .
Find the number of the positive divisors of N! , modulo 10^9+7 .      Constraints  1≤N≤10^3         Input The input is given from Standard Input in the following format:  N       Output Print the number of the positive divisors of N! , modulo 10^9+7 .        Sample Input 1 3      Sample Output 1 4  There are four divisors of 3!  =6 : 1 , 2 , 3 and 6 . Thus, the output should be 4 .       Sample Input 2 6      Sample Output 2 30       Sample Input 3 1000      Sample Output 3 972926972

Solution (Python):
import sys
from sys import exit
from collections import deque
from bisect import bisect_left, bisect_right, insort_left, insort_right
from heapq import heapify, heappop, heappush
from itertools import product, permutations, combinations, combinations_with_replacement
from functools import reduce
from math import gcd, sin, cos, tan, asin, acos, atan, degrees, radians

sys.setrecursionlimit(10**6)
INF = 10**20
eps = 1.0e-20
MOD = 10**9+7

def lcm(x,y):
    return x*y//gcd(x,y)
def lgcd(l):
    return reduce(gcd,l)
def llcm(l):
    return reduce(lcm,l)
def powmod(n,i,mod):
    return pow(n,mod-1+i,mod) if i<0 else pow(n,i,mod)
def div2(x):
    return x.bit_length()
def div10(x):
    return len(str(x))-(x==0)
def intput():
    return int(input())
def mint():
    return map(int,input().split())
def lint():
    return list(map(int,input().split()))
def ilint():
    return int(input()), list(map(int,input().split()))
def judge(x, l=['Yes', 'No']):
    print(l[0] if x else l[1])
def lprint(l, sep='\n'):
    for x in l:
        print(x, end=sep)
def ston(c, c0='a'):
    return ord(c)-ord(c0)
def ntos(x, c0='a'):
    return chr(x+ord(c0))
class counter(dict):
    def __init__(self, *args):
        super().__init__(args)
    def add(self,x,d=1):
        self.setdefault(x,0)
        self[x] += d
    def list(self):
        l = []
        for k in self:
            l.extend([k]*self[k])
        return l
class comb():
    def __init__(self, n, mod=None):
        self.l = [1]
        self.n = n
        self.mod = mod
    def get(self,k):
        l,n,mod = self.l, self.n, self.mod
        k = n-k if k>n//2 else k
        while len(l)<=k:
            i = len(l)
            l.append(l[i-1]*(n+1-i)//i if mod==None else (l[i-1]*(n+1-i)*powmod(i,-1,mod))%mod)
        return l[k]
def pf(x):
    C = counter()
    p = 2
    while x>1:
        k = 0
        while x%p==0:
            x //= p
            k += 1
        if k>0:
            C.add(p,k)
        p = p+2-(p==2) if p*p<x else x
    return C

N=intput()
C=counter()
for x in range(1,N+1):
    s=pf(x)
    for k in s:
        C.add(k,s[k])
ans=1
for k in C:
    ans*=C[k]+1
    ans%=MOD
print(ans)

Solution (Python):
import sys
mod=10**9+7 ; inf=float("inf")
from math import sqrt, ceil
from collections import deque, Counter, defaultdict 
input=lambda: sys.stdin.readline().strip()
sys.setrecursionlimit(11451419)
from decimal import ROUND_HALF_UP,Decimal as D  
  
from functools import lru_cache
from bisect import bisect_left as bileft, bisect_right as biright
from fractions import Fraction as F  






n=int(input())
dp=[0]*1020
dp[1]=1
dp[2]=2
mod=10**9+7
from math import sqrt
def eratosu(n):
  if not isinstance(n,int):
    raise TypeError("nがint型になってねえぞ")
  if n<2:
    raise ValueError('nが2よりちっちぇえぞ')
  prime = []
  limit = sqrt(n)
  data = [i+1 for i in range(1, n)]  
  while True:
    p = data[0]
    if limit <= p:
        return prime + data
    prime.append(p)
    data = [e  for e in data if e % p != 0]
def bunkai(n):
    if n==2: return [[2,1]]
    if n==3: return [[3,1]]
    ans=[]
    temp=n
    
    
    primelist=eratosu( int(sqrt(n)) )
    for i in primelist:
        if temp % i ==0:
            ji=0
            while temp%i==0:
                ji+=1
                temp//=i
            ans.append([i,ji])
    if ans==[]:return([[n,1]])  
    if temp!=1:
        ans.append([temp,1])  
    return ans

NOW=defaultdict(int)
for i in range(2,n+1):
    l=bunkai(i)
    
    for info in l:
        NOW[info[0]]+= info[1]

qq=list(NOW.values())
ans=1
for i in qq:
    ans*=(i+1) 
    ans%=mod
print(ans)

Solution (Python):
def fact(A): 
    c0 = A
    r = 2
    lis = []
    count = 1
    while A != 1:
        if A%r == 0:
            A = A//r
            lis.append(r)
            r = 2
        else:
            r += 1
        if r > int(pow(c0,0.5))+1:
            lis.append(A)
            break
    return(lis)

n = int(input())
mod = 10**9+7

L = [0]*(n+1)
for i in range(1,n+1):
    p = fact(i)
    for q in p:
        L[q] += 1
        
ans = 1
for i in range(1,n+1):
    ans *= L[i] + 1
    ans %= mod
    
print(ans)

Solution (Python):
def resolve():
    '''
    code here
    '''
    N = int(input())

    def get_sieved_list(x):
        dp = [1 if item % 2 == 0 else 0 for item in range(x+1)]
        dp[:3] = [2,1,1]

        for prim_candi in range(3, x+1):
            temp_num = prim_candi
            while temp_num <= x:
                dp[temp_num] += 1
                temp_num += prim_candi
            if prim_candi >= x:
                return [i  for i in range(x+1) if dp[i] == 1]
                
    
    if N > 2:
        factor_filter = set(get_sieved_list(N))
        prime_list = [0 for _ in range(N+1)]
        for i in factor_filter:
            if i >1:
                for j in range(2, N+1):
                    while j >= 1 and j % i == 0:
                        j //= i
                        prime_list[i] += 1

        res = 1
        for item in prime_list:
            res *= (item+1)
            res %= (10**9+7)
    else:
        res = N

    print(res%(10**9+7))

if __name__ == "__main__":
    resolve()

Solution (Python):
import math

n = int(input())

MOD = 10 ** 9 + 7
prime = [0] * (n+1)
yaku = list(range(n+1))

for i in range(n):
    num = i + 1
    
    for j in range(num+1):
        if j <= 1:
            continue
        else:
            if num % j == 0:
                p = j
                yaku[num] = p
                while num > 1:
                    n_num = num // p
                    prime[p] += 1
                    p = yaku[n_num]
                    num = n_num

ans = 1
for p in prime:
    ans *= (p+1)
    ans %= MOD

print(ans)

Solution (Python):
N = int(input())

cnt=[0]*(10**3+1)

for dam in range(2,N+1):
    
    pf={}
    m=dam
    for i in range(2,int(m**0.5)+1):
        while m%i==0:
            pf[i]=pf.get(i,0)+1
            m//=i
    if m>1:pf[m]=1
    
    
    for key in pf:
        cnt[key]+=pf[key]

out=1
for i in range(2,10**3+1):
    out*=(cnt[i]+1)
print(out % (10**9+7))

Solution (Python):
n = int(input())
factors = {}

for i in range(2, n+1):
    p = i

    while p > 1:
        f = False
        for j in range(2, int(p**0.5)+1):
            if p % j == 0:
                if j in factors:
                    factors[j] += 1
                else:
                    factors[j] = 1

                p //= j
                f = True
                break

        if not f:
            if p in factors:
                factors[p] += 1
            else:
                factors[p] = 1
            break

ans = 1
for f in factors.values():
    ans *= f+1

print(ans % 1000000007)

Solution (Python):
def getN():
    return int(input())
def getNM():
    return map(int, input().split())
def getList():
    return list(map(int, input().split()))
def getArray(intn):
    return [int(input()) for i in range(intn)]
def input():
    return sys.stdin.readline().rstrip()
def rand_N(ran1, ran2):
    return random.randint(ran1, ran2)
def rand_List(ran1, ran2, rantime):
    return [random.randint(ran1, ran2) for i in range(rantime)]
def rand_ints_nodup(ran1, ran2, rantime):
  ns = []
  while len(ns) < rantime:
    n = random.randint(ran1, ran2)
    if not n in ns:
      ns.append(n)
  return sorted(ns)

def rand_query(ran1, ran2, rantime):
  r_query = []
  while len(r_query) < rantime:
    n_q = rand_ints_nodup(ran1, ran2, 2)
    if not n_q in r_query:
      r_query.append(n_q)
  return sorted(r_query)

from collections import defaultdict, deque, Counter
from sys import exit
from decimal import *
from heapq import heapify, heappop, heappush
import math
import random
import string
from copy import deepcopy
from itertools import combinations, permutations, product
from operator import mul, itemgetter
from functools import reduce
from bisect import bisect_left, bisect_right

import sys
sys.setrecursionlimit(1000000000)
mod = 10 ** 9 + 7





class Osa_k():
    def __init__(self, n):
        self.sieve = list(range(n + 1))
        self.sieve[0] = 1 
        self.sieve[1] = 1 
        m = int(math.sqrt(n))
        for i in range(2, m + 1):
            if self.sieve[i] < i:
                continue
            for j in range(i * i, n + 1, i):
                if self.sieve[j] == j:
                    self.sieve[j] = i

    def factorize(self, n):
        prime = defaultdict(int)
        if n == 0 or n == 1:
            return (n, 1)
        opt = n
        while opt > 1:
            prime[self.sieve[opt]] += 1
            opt //= self.sieve[opt]
        return sorted(prime.items())

N = getN()
O = Osa_k(10 ** 6 + 1)

prime = defaultdict(int)
for i in range(2, N + 1):
    for j in O.factorize(i):
        prime[j[0]] += j[1]

ans = 1
for i in prime.items():
    ans *= i[1] + 1
    ans %= mod
print(ans)

Solution (Python):
N=int(input())
from collections import defaultdict
p=defaultdict(int)
def f(n):
    for i in range(2,int(n**.5)+1):
        x=0
        while n%i==0:
            n//=i
            x+=1
        if x:
            p[i]+=x
    if n>1:
        p[n]+=1
for i in range(2,N+1):
    f(i)
from functools import reduce
print(reduce(lambda x,y:x*(y+1),p.values(),1)%(10**9+7))

Solution (Python):







def prime_factorization(n):
    table = []
    for x in range(2, int(n ** 0.5) + 1):
        while n % x == 0:
            table.append(x)
            n //= x
    if n > 1:
        table.append(n)
    return table


N = int(input())
MOD = 10**9+7

mp = [0]*1000
for i in range(2, N+1):
    pf = prime_factorization(i)
    for p in pf:
        mp[p] += 1

ans = 1
for p in mp:
    if p == 0:
        continue

    ans = ans*(p+1)

print(ans % MOD)

Solution (Python):
def prime_factorization(n):
    table = []
    for x in range(2, int(n ** 0.5) + 1):
        while n % x == 0:
            table.append(x)
            n //= x
    if n > 1:
        table.append(n)
    return table


N = int(input())
MOD = 10**9+7

mp = [0]*1000
for i in range(2, N+1):
    pf = prime_factorization(i)
    for p in pf:
        mp[p] += 1

ans = 1
for p in mp:
    if p == 0:
        continue

    ans = ans*(p+1)

print(ans % MOD)

Solution (Python):
N = int(input())

mod = 10**9+7
so = [0]*N

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

for i in range(2, N+1):
    arr = factorization(i)
    for a in arr:
        so[a[0]-1] += a[1]

ans = 1
for s in so:
    ans *= s+1
    ans %= mod

print(ans)

Solution (Python):

import sys

sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read

from collections import defaultdict
sys.setrecursionlimit(10**7)
import math








INF = 1 << 50

class factorials:
    '''
    args:
      n : max val when exploring factorials
    '''
    def __init__(self, n=1):
        self.n = 1
        self.factorials = []
        self.update_factorials(n)

    def update_factorials(self, n):
        if self.n >= n:
            return None
        for i in range(self.n+1, n+1):
            done = False
            limit = int(i ** 0.5)
            for j in self.factorials:
                if j > limit: break
                if not i % j:
                    done = True
                    break
            if not done:
                self.factorials.append(i)
        self.n = n
        return None

    def factorials_list(self):
        return self.factorials

    def check_fact(self, x):
        if x > self.n**2:
            self.update_factorials(int(x ** 0.5)+1)
        for f in self.factorials:
            if not x % f:
                return False
        return True

    def prime_factorization(self, val, divisors=None):
        
        max_n = int(math.sqrt(val))
        if self.n < max_n:
            self.update_factorials(max_n)
        if divisors == None:
            divisors = defaultdict(lambda: 0)
        for f in self.factorials:
            if f > val: break
            while True:
                if not val % f:
                    divisors[f] += 1
                    val //= f
                else:
                    break
        if val > 1:
            divisors[val] += 1
        return divisors

def run():
    N = int(input())
    FACT = factorials()
    max_n = int(math.sqrt(N))
    divisors = defaultdict(lambda: 0)
    for n in range(2, N+1):
        divisors = FACT.prime_factorization(n, divisors)
    
    mod = 10 ** 9 + 7
    ans = 1
    for key, value in divisors.items():
        ans *= value+1
        ans %= mod
    print(ans)

if __name__ == "__main__":
    run()

Solution (Python):

import sys

sysread = sys.stdin.buffer.readline
read = sys.stdin.buffer.read

from collections import defaultdict
sys.setrecursionlimit(10**7)
import math








INF = 1 << 50

def factorials(n):
    facts = []
    for k in range(2, n+1):
        done = False
        max_f = int(math.sqrt(k))
        for f in facts:
            if f > max_f:break
            if not k % f:
                done = True
                break
        if not done:
            facts.append(k)
    return facts

def prime_factorization(val, facts = None, divisors = None):
    if facts == None:
        max_n = int(math.sqrt(val))
        facts = factorials(max_n)
    if divisors == None:
        divisors = defaultdict(lambda:0)
    for f in facts:
        if f > val:break
        while True:
            if not val % f:
                divisors[f] += 1
                val //= f
            else:
                break
    if val > 1:
        divisors[val] += 1

    return divisors

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

    max_n = int(math.sqrt(N))
    facts = factorials(max_n)
    divisors = defaultdict(lambda: 0)
    for n in range(2, N+1):
        divisors = prime_factorization(n, facts, divisors)
    
    mod = 10 ** 9 + 7
    ans = 1
    for key, value in divisors.items():
        ans *= value+1
        ans %= mod
    print(ans)

if __name__ == "__main__":
    run()

Solution (Python):
N = int(input())
prime_cnt = [0] * 1000
ans = 0
for i in range(2, N + 1):
    work = i
    for j in range(2, int(i ** (1 / 2)) + 1):
        while work % j == 0:
            prime_cnt[j - 1] += 1
            work //= j
    if work != 1:
        prime_cnt[work - 1] += 1

ans = 1
mod = 10 ** 9 + 7
for cnt in prime_cnt:
    if cnt:
        ans *= (cnt + 1)
        ans %= mod
print(ans)

Solution (Python):
N=int(input())
divisor=[0]*(N+1)
count=[0]*(N+1)
for i in range(2,N+1):
    if divisor[i]:
        continue
    j=1
    while i*j<=N:
        divisor[i*j]=1
        now=i*j
        while now%i==0:
            count[i]+=1
            now//=i
        j+=1
ans=1
M=10**9+7
for i in range(N+1):
        ans*=(count[i]+1)
        ans%=M
print(ans)

Solution (Python):
import math
from collections import defaultdict
N = int(input())
mod = 10 ** 9 + 7
d = defaultdict(int)

if (N == 1):
    print(1)
    exit()

for n in range(1, N + 1):
    for i in range(2, math.ceil(n ** 0.5) + 1):
        while n % i == 0:
            n //= i
            d[i] += 1

    if (n != 1):
        d[n] += 1

ans = 1
for i in d.values():
    ans *= (i + 1) % mod
    ans %= mod

print(ans)

Solution (Python):
import sys
from collections import defaultdict

read = sys.stdin.read
readline = sys.stdin.buffer.readline
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7


def main():
    N = int(readline())
    if N == 1:
        print(1)
        sys.exit()
    div = defaultdict(int)
    for n in range(1, N + 1):
        for i in range(2, int(n ** 0.5) + 1):
            while n % i == 0:
                n //= i
                div[i] += 1
        if n != 1:
            div[n] += 1

    ans = 1
    for Value in div.values():
        ans *= (Value+1) % MOD
        ans %= MOD
    print(ans)


if __name__ == '__main__':
    main()

Solution (Python):
from collections import Counter

n = int(input())
c = Counter()


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

for i in range(1, n + 1):
    c.update(prime_factorize(i))
    
ans = 1
mod = 10**9+7
for v in c.values():
    ans *= v + 1
    ans %= mod 

print(ans)

Solution (Python):






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





mydict = {}
for i in range(1,N+1):
    mylist = factorization(i)
    for x in mylist:
        if x[0] in mydict.keys():
            mydict[x[0]] += x[1]
        else:
            mydict[x[0]] = x[1]
ans = 1
for j,y in mydict.items():
    if j > 1:
        ans *= y+1
print(ans%(10**9+7))

Solution (Python):
n = int(input())
val = [1 for _ in range(n)]
ans = 1
for i in range(2, n+1):
    for j in range(2, i+1):
        while i%j == 0:
            val[j-1] += 1
            i //= j
    if i != 1:
        val[i-1] += 1

for i in val:
    ans *= i
    ans %= 10**9+7
print(ans)

Solution (Python):
from sys import stdin
nii=lambda:map(int,stdin.readline().split())
lnii=lambda:list(map(int,stdin.readline().split()))
from collections import Counter

def factorization(n):
    p=2
    fcr=[]
    while p*p<=n:
        while n%p==0:
            fcr.append(p)
            n//=p
        p+=1
    if n>1:
        fcr.append(n)
    return fcr

n=int(input())

mod=10**9+7

l=[]
for i in range(1,n+1):
  l+=factorization(i)

c=Counter(l)
ans=1
for i in c:
  ans*=(c[i]+1)
  ans%=mod

print(ans)

Solution (Python):

n = int(input())
def count(x):
    c = 0
    t = n
    while t:
        c += t//x
        t //= x
    return c +1
limit = int(n**0.5)
ans = count(2)
if n < 3:
    print(ans)
    exit()
data = [i + 1 for i in range(2, n, 2)]
while data:
    p = data[0]
    ans *= count(p)
    ans %= 10**9 + 7
    data = [e for e in data if e % p != 0]
print(ans)

Solution (Python):

n = int(input())
def count(x):
    c = 0
    t = n
    while t:
        c += t//x
        t //= x
    return c +1
prime = [2]
limit = int(n**0.5)
ans = count(2)
if n < 3:
    print(ans)
    exit()
data = [i + 1 for i in range(2, n, 2)]
while True:
    p = data[0]
    if limit < p:
        for i in data:
            ans *= count(i)
            ans %= 10**9+7
        break
    ans *= count(p)
    ans %= 10**9 + 7
    data = [e for e in data if e % p != 0]
print(ans)

Solution (Python):
def p_factorization(n):
    if n == 1: return {}
    pf_cnt = {}
    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
            pf_cnt[i] = cnt

    if temp != 1: pf_cnt[temp] = 1
    return pf_cnt


n = int(input())
pf_cnts = {}
for i in range(2,n+1):
    i_pf_cnt = p_factorization(i)
    for k,v in i_pf_cnt.items():
        pf_cnts.setdefault(k,0)
        pf_cnts[k] += v

MOD = 10**9+7  
ans = 1
for k,v in pf_cnts.items():
    ans *= (v+1)
    ans %= MOD                       

print(ans)

Solution (Python):
MOD = 10 ** 9 + 7
n = int(input())
d = {}
for i in range(1, n + 1):
    j = 2
    while j * j <= i:
        while i % j == 0:
            if j in d:
                d[j] += 1
            else:
                d.setdefault(j, 1)
            i //= j
        j += 1
    if i != 1:
        if i in d:
            d[i] += 1
        else:
            d.setdefault(i, 1)
m = 1
for v in d.values():
    m *= v + 1
print(m % MOD)

Solution (Python):
import sys

N = int(sys.stdin.readline())
mod = 10**9 + 7

values = [i for i in range(N+1)]
factors = {}
exists = set()
for i in range(2, N+1):
    if i not in factors:
        factors[i] = 0
    for j in range(i, N+1, i):
        tmp = values[j]
        while tmp % i == 0:
            factors[i] += 1
            tmp //= i
        values[j] = tmp



ans = 1
for factor, count in factors.items():
    ans *= count + 1
    ans %= mod

print(ans)

Solution (Python):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())
mod = 10**9+7
from collections import Counter

def prime_factorize(n):
    a = []
    while n % 2 == 0:
        primes.append(2)
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            primes.append(f)
            n //= f
        else:
            f += 2
    if n != 1:
        primes.append(n)
    return a
primes = []
for i in range(1, N+1):
    prime_factorize(i)
c = Counter(primes)
ans = 1
for n, cnt in c.most_common():
    ans *= (cnt+1)
    ans %= mod
print(ans)

Solution (Python):
p = 10**9+7
P = [1 for _ in range(1000)]
P[0]=0
P[1]=0
for i in range(2,35):
    for j in range(i**2,1000,i):
        P[j]=0
Q = []
for i in range(2,1000):
    if P[i]==1:
        Q.append(i)
N = int(input())
C = {q:0 for q in Q}
for i in range(2,N+1):
    x = i
    for q in Q:
        if x%q==0:
            while x%q==0:
                x = x//q
                C[q] += 1
cnt = 1
for q in Q:
    cnt = (cnt*(C[q]+1))%p
print(cnt)

Solution (Python):
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]]

mod = 10 ** 9 + 7
N = int(input())

P = primes(N)

ans = 1

for p in P:
    cnt = 1
    tmp = p
    while tmp <= N:
        cnt += N // tmp
        tmp *= p
    ans *= cnt
    ans %= mod

print(ans)

Solution (Python):
MOD = 10 ** 9 + 7
n = int(input())

div = [1 for _ in range(n + 1)]
for num in range(2, n + 1):
    for i in range(2, int(num ** 0.5) + 1):
        while num % i == 0:
            div[i] += 1
            num //= i
    if num != 1:
        div[num] += 1

ans = 1

for num in div:
    ans *= num
    ans %= MOD
print(ans)

Solution (Python):

def Prime_Factorization(N):
    if N<0:
        R=[[-1,1]]
    else:
        R=[]

    N=abs(N)
    k=2
    while k*k<=N:
        if N%k==0:
            C=0
            while N%k==0:
                C+=1
                N//=k
            R.append([k,C])
        k+=1

    if N!=1:
        R.append([N,1])
    if not R:
        R.append([N,1])

    return R

N=int(input())

if N==1:
    print(1)
else:
    D={}
    for k in range(2,N+1):
        T=Prime_Factorization(k)
        for p,e in T:
            if p in D:
                D[p]+=e
            else:
                D[p]=e

    M=10**9+7
    X=1
    for p in D:
        X*=D[p]+1
        X%=M
    print(X)

Solution (Python):
import sys
import math
import copy
import heapq
from functools import cmp_to_key
from bisect import bisect_left, bisect_right
from collections import defaultdict, deque, Counter



input = sys.stdin.readline
getS = lambda: input().strip()
getN = lambda: int(input())
getList = lambda: list(map(int, input().split()))
getZList = lambda: [int(x) - 1 for x in input().split()]

INF = float("inf")
MOD = 10**9 + 7
divide = lambda x: pow(x, MOD-2, MOD)

def nck(n, k, kaijyo):
    return (npk(n, k, kaijyo) * divide(kaijyo[k])) % MOD

def npk(n, k, kaijyo):
    if k == 0 or k == n:
        return n % MOD
    return (kaijyo[n] * divide(kaijyo[n-k])) % MOD

def fact_and_inv(SIZE):
    inv = [0] * SIZE  
    fac = [0] * SIZE  
    finv = [0] * SIZE  
    inv[1] = 1
    fac[0] = fac[1] = 1
    finv[0] = finv[1] = 1
    for i in range(2, SIZE):
        inv[i] = MOD - (MOD // i) * inv[MOD % i] % MOD
        fac[i] = fac[i - 1] * i % MOD
        finv[i] = finv[i - 1] * inv[i] % MOD

    return fac, finv

def renritsu(A, Y):
    
    
    
    A = np.matrix(A)
    Y = np.matrix(Y)
    Y = np.reshape(Y, (-1, 1))
    X = np.linalg.solve(A, Y)

    
    return X.flatten().tolist()[0]

class TwoDimGrid:
    
    def __init__(self, h, w, wall="
        self.h = h
        self.w = w
        self.size = (h+2) * (w+2)
        self.wall = wall
        self.get_grid()
        

    def get_grid(self):
        grid = [self.wall * (self.w + 2)]
        for i in range(self.h):
            grid.append(self.wall + getS() + self.wall)

        grid.append(self.wall * (self.w + 2))
        self.grid = grid
    def init_cost(self):
        self.cost = [INF] * self.size

    def pos(self, x, y):
        
        return y * (self.w + 2) + x
    def getgrid(self, x, y):
        return self.grid[y][x]
    def get(self, x, y):
        return self.cost[self.pos(x, y)]
    def set(self, x, y, v):
        self.cost[self.pos(x, y)] = v
        return
    def show(self):
        for i in range(self.h+2):
            print(self.cost[(self.w + 2) * i:(self.w + 2) * (i+1)])
    def showsome(self, tgt):
        for t in tgt:
            print(t)
        return
    def showsomejoin(self, tgt):
        for t in tgt:
            print("".join(t))
        return

    def search(self):
        grid = self.grid
        move = [(0, 1), (0, -1), (1, 0), (-1, 0)]
        move_eight = [(0, 1), (0, -1), (1, 0), (-1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
        
        
        
        
        

def bun(n):
    ret = defaultdict(int)
    for i in range(2, int(n//2 + 2)):
        while(n%i == 0):
            ret[i] += 1
            n //= i

    if len(ret.keys()) == 0:
        return {n: 1}
    else:
        return ret

def solve():
    n = getN()
    d = defaultdict(int)
    for i in range(2, n+1):
        for k, v in bun(i).items():
            d[k] += v

    ans = 1
    
    for v in d.values():
        ans *= (v+1)
        ans %= MOD
    print(ans)


def main():
    n = getN()
    for _ in range(n):
        solve()

    return
if __name__ == "__main__":
    
    solve()

Solution (Python):
from collections import defaultdict


def factorize(N):  
    p = 2
    while p * p <= N:
        if N % p == 0:
            N //= p
            d[p] += 1
        else:
            p += 1
    if N > 1:
        d[N] += 1
    return



n = int(input())
mod = 10 ** 9 + 7

d = defaultdict(int)
for i in range(1, n + 1):
    factorize(i)

ans = 1
for cnt in d.values():
    ans = ans * (cnt + 1) % mod
print(ans)

Solution (Python):
import math
N = int(input())
d = {}

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

  if temp!=1:
    if temp in d:
      d[temp] += 1
    else:
      d[temp] = 1
    arr.append(temp)

  if arr==[]:
    if n in d:
      d[n] += 1
    else:
      d[n] = 1
    
for i in range(2, N+1):
  main(i)
ans = 1
for i in d.values():
  ans *= (i+1)
ans = ans % (10**9+7)
print(ans)

Solution (Python):


n = int(input())


def PrimeFactorization(n):
    ret = []
    for i in range(2, int(n ** 0.5)+1):
        if n % i != 0:
            continue
        
        exp = 0
        while n % i == 0:
            exp += 1
            n //= i
        
        ret.append([i, exp])

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

    return ret

a = [0]*(n+1)
for i in range(2, n+1):
    tmp = PrimeFactorization(i)
    for j in range(len(tmp)):
        a[tmp[j][0]] += tmp[j][1]


ret = 1

for i in a:
    ret *= (i+1)
    ret %= 1000000007

print(ret)

Solution (Python):
import sys
def input(): return sys.stdin.readline().strip()
def mapint(): return map(int, input().split())
sys.setrecursionlimit(10**9)

N = int(input())
mod = 10**9+7
def prime_factorize(n):
    a = []
    while n % 2 == 0:
        primes[2]+=1
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            primes[f]+=1
            n //= f
        else:
            f += 2
    if n != 1:
        primes[n]+=1
    return

primes = [0]*(N+1)
for i in range(1, N+1):
    prime_factorize(i)
ans = 1
for p in primes:
    ans *= (p+1)
    ans %= mod
print(ans)

Solution (Python):


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())
MOD = 10**9+7

d = {}

for i in range(2, N+1):
    D = factorization(i)
    for n in D:
        if n[0] in d: d[n[0]] += n[1]
        else: d[n[0]] = n[1]

ret = 1

for k, v in d.items():
    ret *= v + 1

print(ret%MOD)

Solution (Python):


from fractions import gcd

from collections import Counter, deque, defaultdict
from heapq import heappush, heappop, heappushpop, heapify, heapreplace, merge
from bisect import bisect_left, bisect_right, bisect, insort_left, insort_right, insort
from itertools import accumulate, product, permutations, combinations, combinations_with_replacement
import math

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 = Counter(prime_factorize(math.factorial(N)))

ret = 1
for key, item in c.items():
    ret = ret * (item+1)
print(ret % (10**9 +7))

Solution (Python):
n=int(input())
d={i:0 for i in range(n+1)}
for i in range(2,n+1):
    for j in range(2,int(i**0.5)+1):
        while i%j==0:
            i//=j
            d[j]+=1
    if i!=1:
        d[i]+=1
a=1
mod=10**9+7
for i in d.values():
    a=a*(i+1)%mod
print(a)

Solution (Python):
n=int(input())
MOD=10**9+7
cnt=[0 for _ in range(1000)]
for i in range(2,n+1):
    e=i
    for j in range(2,i+1):
        while(e%j==0):
            e//=j
            cnt[j]+=1
ans=1
for i in range(1000):
    ans=(ans*(cnt[i]+1))%MOD
print(ans)

Solution (Python):
import sys
input = sys.stdin.readline



def get_prime(N):
    prime = dict()
    prime[1] = 1
    i = 2
    while i * i <= N:
        while N % i == 0:
            if i in prime.keys():
                prime[i] += 1
            else:
                prime[i] = 1
            N = N // i
        i += 1
    if N != 1:
        prime[N] = 1
    return prime


def main():
    N = int(input().strip())
    div_table = [0] * (N + 1)
    MOD = 10**9 + 7
    ans = 1
    for i in range(2, N + 1):
        for j in range(i, N + 1, i):
            div_table[j] += 1

    prime = dict()
    for i in range(2, N + 1):
        if div_table[i] == 1:
            prime[i] = 0

    for i in range(2, N + 1):
        _prime = get_prime(i)
        for k, v in _prime.items():
            if k == 1:
                continue
            prime[k] += v

    for k, v in prime.items():
        ans *= v + 1
        ans %= MOD

    print(ans)


if __name__ == "__main__":
    main()