Hướng dẫn proper positive divisors python - số chia dương thích hợp python

Chức năng Python: Bài tập-11 với giải pháp

Viết chức năng Python để kiểm tra xem một số có hoàn hảo hay không.

Theo Wikipedia: Theo lý thuyết số, một số hoàn hảo là một số nguyên dương bằng tổng số các giao diện dương hợp lý của nó, nghĩa là tổng số các giao diện dương của nó không bao gồm chính số (còn được gọi là tổng hợp của nó). Tương tự, một số hoàn hảo là một số là một nửa tổng của tất cả các ước số dương của nó (bao gồm cả chính nó). Ví dụ & NBSP; 1 + 2 + 3 + 6) / 2 = 6. Số hoàn hảo tiếp theo là 28 = 1 + 2 + 4 + 7 + 14. Điều này được theo sau bởi các số hoàn hảo 496 và 8128.
Example : The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128.

Giải pháp mẫu:-:-

Mã Python:

def perfect_number(n):
    sum = 0
    for x in range(1, n):
        if n % x == 0:
            sum += x
    return sum == n
print(perfect_number(6))
 

Đầu ra mẫu:

True

Trình bày bằng hình ảnh:

Sơ đồ:

Trực quan hóa thực thi mã Python:

Công cụ sau đây trực quan hóa những gì máy tính đang làm từng bước khi nó thực hiện chương trình đã nói:

Trình chỉnh sửa mã Python:

Có một cách khác để giải quyết giải pháp này? Đóng góp mã của bạn (và nhận xét) thông qua Disqus.

Trước đây: Viết chương trình Python để in các số chẵn từ một danh sách đã cho. Write a Python program to print the even numbers from a given list.
Next: Write a Python function that checks whether a passed string is palindrome or not.

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Đọc
Examples: 

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Bàn luậnSimple Solution is to go through every number from 1 to n-1 and check if it is a divisor. Maintain sum of all divisors. If sum becomes equal to n, then return true, else return false.
An Efficient Solution is to go through numbers till square root of n. If a number ‘i’ divides n, then add both ‘i’ and n/i to sum. 
Below is the implementation of efficient solution. 
 

C++

#include<iostream>

Một số là một con số hoàn hảo nếu bằng tổng số các giao diện thích hợp của nó, nghĩa là tổng số các ước số dương của nó không bao gồm chính số. Viết một hàm để kiểm tra xem một số đã cho có hoàn hảo hay không. & NBSP; Ví dụ: & nbsp;

Một giải pháp đơn giản là đi qua mỗi số từ 1 đến N-1 và kiểm tra xem đó có phải là một ước số không. Duy trì tổng của tất cả các ước. Nếu tổng trở nên bằng n, thì trả về true, nếu không trả về false. Một giải pháp hiệu quả là đi qua các số cho đến căn bậc hai của n. Nếu một số ‘I, chia n, thì hãy thêm cả‘ I, và N/I vào tổng. & Nbsp; bên dưới là việc thực hiện giải pháp hiệu quả. & Nbsp; & nbsp;

True

using namespace std;

bool

True

True

True

True

True

True

True

True

True

True

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

True

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

#include<iostream>1#include<iostream>2 #include<iostream>3#include<iostream>4

True

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15 Output: false Divisors of 15 are 1, 3 and 5. Sum of divisors is 9 which is not equal to 15. Input: n = 6 Output: true Divisors of 6 are 1, 2 and 3. Sum of divisors is 6.0Input: n = 15 Output: false Divisors of 15 are 1, 3 and 5. Sum of divisors is 9 which is not equal to 15. Input: n = 6 Output: true Divisors of 6 are 1, 2 and 3. Sum of divisors is 6.1 namespace4

True

Java

std;3 std;4

True

True

std;6 std;7

True

True

True

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

True

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Python3

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Java

std;3 std;4

True

std;6 std;7

True

True

True

True

True

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

True

C#

True

True

Java

True

std;3 std;4

True

True

True

std;6 std;7

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

True

True

True

True

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True 6>>> import collections >>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7]) >>> A Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1}) >>> A.most_common(1) [(3, 4)] >>> A.most_common(3) [(3, 4), (1, 2), (2, 2)] 2 >>> import collections >>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7]) >>> A Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1}) >>> A.most_common(1) [(3, 4)] >>> A.most_common(3) [(3, 4), (1, 2), (2, 2)] 3True 3 namespace1

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

Java

True

True

std;3 std;4

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

JavaScript

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

True

>>> import collections

>>> A = collections.Counter([1, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7])
>>> A
Counter({3: 4, 1: 2, 2: 2, 4: 1, 5: 1, 6: 1, 7: 1})
>>> A.most_common(1)
[(3, 4)]
>>> A.most_common(3)
[(3, 4), (1, 2), (2, 2)]

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Input: n = 15
Output: false
Divisors of 15 are 1, 3 and 5. Sum of 
divisors is 9 which is not equal to 15.

Input: n = 6
Output: true
Divisors of 6 are 1, 2 and 3. Sum of 
divisors is 6.

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

True

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Output:   
 

Below are all perfect numbers till 10000
6 is a perfect number
28 is a perfect number
496 is a perfect number
8128 is a perfect number

Độ phức tạp về thời gian: O (√n) O(√n)

Không gian phụ trợ: O (1), vì không có thêm dung lượng nào được lấy. Hãy là một số sự thật thú vị về các số hoàn hảo: & nbsp; 1) Mỗi ​​số hoàn hảo là của Mẫu 2p? ;? muốn chia sẻ thêm thông tin về chủ đề được thảo luận ở trên & NBSP;O(1), since no extra space has been taken.
Below are some interesting facts about Perfect Numbers: 
1) Every even perfect number is of the form 2p?1(2p ? 1) where 2p ? 1 is prime. 
2) It is unknown whether there are any odd perfect numbers.
References: 
https://en.wikipedia.org/wiki/Perfect_number
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above