Python Challenges: Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers
Python Challenges - 1: Exercise-47 with Solution
Write a Python program to find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.
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:
from functools import reduce
from itertools import combinations_with_replacement as combinations
MAX_NUM = 28123
def divisors(x):
return set(reduce(list.__add__, [[div, x//div] for div in range(2, int(x**0.5) + 1) if x % div == 0] + [[1]]))
def abundant(nums):
return sum(divisors(nums)) > nums
abundant_nums = (n for n in range(1, MAX_NUM) if abundant(n))
sum_of_two_abundants = set(a + b for a, b in combinations(abundant_nums, 2))
not_abundant_nums = (x for x in range(MAX_NUM) if x not in sum_of_two_abundants)
print(sum(not_abundant_nums))
Sample Output:
4179871
Flowchart:
Python Code Editor:
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Previous: Write a Python program to compute the sum of all the amicable numbers under a given number.
Next: Write a Python program to find the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
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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
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