Посчитать кол-во чисел со всевозможными кол-вами делителей

def prns(n):
    list_true = [True] * n
    for o in range(3, (int(n ** 0.5) + 1), 2):
        if list_true[o]:
            list_true[o * o::2 * o] = [False] * ((n - o * o - 1) // (2 * o) + 1)
    return [2] + [u for u in range(3, n, 2) if list_true[u]]
 
 
def check(n):
    if n & 1 == 0:
        return False
    d = 3
    while d * d <= n:
        if n % d == 0:
            return False
        d = d + 2
    return True
 
 
def solution():
    counter = 0
    e = int(input())
    f = int(input())
    prn = prns(int(f ** 0.5))
    for n in range(e, f + 1):
        for i in prn:
            if (i * i < n and not n % i and
                    check(n // i)):
                counter += 1
                break
    print(counter)
 
 
solution()

from itertools import chain, groupby
 
num_of_div = 20
res_dict = {}
 
divs = lambda n: chain(*((d, n // d) for d in range(1, int(n ** 0.5) + 1) if n % d == 0))
lst =[list(set(i)) for i in[list(divs(i)) for i in range(1, num_of_div)]]
 
for i in range(1, num_of_div):
    res_dict["Делителей на {}".format(i)] = 0
 
for i in lst:
    for k in range(1, num_of_div):
        if k in i:
            res_dict["Делителей на {}".format(k)] += 1
 
print(res_dict)

from itertools import chain, groupby
from collections import Counter
 
num_of_div = 1000000
 
divs = lambda n: chain(*((d, n // d) for d in range(1, int(n ** 0.5) + 1) if n % d == 0))
lst =[list(set(i)) for i in[list(divs(i)) for i in range(1, num_of_div)]]
print(dict(Counter([len(i) for i in lst])))

print(dict(__import__("collections").Counter([len(i) for i in[list(set(i)) for i in[list((lambda n: __import__("itertools").chain(*((d, n // d) for d in range(1, int(n ** 0.5) + 1) if n % d == 0)))(i)) for i in range(1, 1000)]]])))

from collections import Counter
from math import log
import numpy as np
def primes(n):
    nn = int(np.sqrt(n)) + 1
    pr = np.ones(nn, dtype = 'int')
    for p in range(3, int(np.sqrt(nn)) + 1, 2) :
        if pr[p] :
            pr[np.arange(p*p, nn, 2*p)] = 0
    res = np.array(np.nonzero(pr)).ravel()
    res = res[(res%2 == 1),]
    res[0,] = 2
    return res 
 
def main():
    k = 1000000
    pr = primes(k)
    arr = np.arange(1, k + 1)
    res = np.ones(k, dtype=int, order='F')
    for p in pr:
        tmp = np.ones(k, dtype=int, order='F')
        npow = int(log(k, p)) + 1
        for i in range(1, npow):
            tmp[(arr%p == 0)] += 1
            arr[(arr%p == 0)] //= p
        res = np.multiply(tmp, res)
    arr[(arr > 1)] = 2
    res = np.multiply(arr, res)
    res = Counter(res.tolist())
    print(sorted(res.items()))
 
main()

def prns(n):
    list_true = [True] * n
    for o in range(3, (int(n ** 0.5) + 1), 2):
        if list_true[o]:
            list_true[o * o::2 * o] = [False] * ((n - o * o - 1) // (2 * o) + 1)
    return [2] + [u for u in range(3, n, 2) if list_true[u]]

from collections import Counter
from math import log
import numpy as np
import matplotlib.pyplot as plt
 
 
def primes(n):
    nn = int(np.sqrt(n)) + 1
    pr = np.ones(nn, dtype='int')
    for p in range(3, int(np.sqrt(nn)) + 1, 2):
        if pr[p]:
            pr[np.arange(p * p, nn, 2 * p)] = 0
    res = np.array(np.nonzero(pr)).ravel()
    res = res[(res % 2 == 1)]
    res[0] = 2
    return res
 
 
def main():
    k = int(input())
    pr = primes(k)
    arr = np.arange(1, k + 1)
    res = np.ones(k, dtype=int, order='F')
 
    for p in pr:
        tmp = np.ones(k, dtype=int, order='F')
        npow = int(log(k, p)) + 1
 
        for i in range(1, npow):
            tmp[(arr % p == 0)] += 1
            arr[(arr % p == 0)] //= p
 
        res = np.multiply(tmp, res)
 
    arr[(arr > 1)] = 2
    res = np.multiply(arr, res)
    res = Counter(res.tolist())
    solution = sorted(res.items())
    for group_ in solution:
        print(f"Количество чисел с {group_[0]} делителем: {group_[1]}")
 
    fig, ax = plt.subplots()
    ax.set_facecolor('seashell')
    fig.set_facecolor('floralwhite')
    fig.set_figwidth(12)
    fig.set_figheight(6)
    ax.set_ylabel("Количество чисел")
    ax.set_title("Количество делителей")
    x_s = [group_[0] for group_ in solution]
    # plt.xticks(np.arange(0, max(x_s) + 1, 5))
    y_s = [group_[1] for group_ in solution]
    # plt.yticks(np.arange(0, max(y_s) + 1, 10000))
 
    for group_ in solution:
        x = group_[0]
        y = group_[1]
        ax.bar(x, y)
 
    plt.show()
 
 
main()