Python Challenges: Compute the sum of all the amicable numbers under a given number

Last update on May 28 2022 13:42:21 (UTC/GMT +8 hours)

Python Challenges - 1: Exercise-46 with Solution

Write a Python program to compute the sum of all the amicable numbers under a given number.

From Wikipedia - Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

Sample Solution:

Python Code:

def amicable_sum(num):
	divisor_sum = [0] * num
	for i in range(1, len(divisor_sum)):
		for j in range(i * 2, len(divisor_sum), i):
			divisor_sum[j] += i	
	# Find all amicable pairs 
	result = 0
	for i in range(1, len(divisor_sum)):
		j = divisor_sum[i]
		if j != i and j < len(divisor_sum) and divisor_sum[j] == i:
			result += i
	return str(result)

print(amicable_sum(500))
print(amicable_sum(10000))

Sample Output:

504
31626

Flowchart:

Python Code Editor:

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Previous: Write a Python program to find the sum of the digits of a given number.
Next: Write a Python program to find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

The os and os.path modules.
The __file__ constant
os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
os.path.dirname(path) (returns "the directory name of pathname path")
os.getcwd() (returns "a string representing the current working directory")
os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m