PyPE solution to PE problem 23
PyPE solution to PE problem 23
Blueprint information
- Status:
- Started
- Approver:
- None
- Priority:
- Undefined
- Drafter:
- None
- Direction:
- Needs approval
- Assignee:
- None
- Definition:
- Approved
- Series goal:
- None
- Implementation:
-
Beta Available
- Milestone target:
- None
- Started by
- Scott Armitage
- Completed by
Whiteboard
ProjectEule
===
A perfect number is a number for which the sum of its proper divisors is
exactly equal to the number. For example, the sum of the proper divisors
of 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect
number.
A number n is called deficient if the sum of its proper divisors is less
than n and it is called abundant if this sum exceeds n.
As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
number that can be written as the sum of two abundant numbers is 24. By
mathematical analysis, it can be shown that all integers greater than 28123
can be written as the sum of two abundant numbers. However, this upper limit
cannot be reduced any further by analysis even though it is known that the
greatest number that cannot be expressed as the sum of two abundant numbers
is less than this limit.
Find the sum of all the positive integers which cannot be written as the sum
of two abundant numbers.
Solution
--------
We generate a list of all abundant numbers less than the known limit. From
this list, we create a set of all possible sums of two abundant numbers
from within the list. We take care to also account for cases where a=b.
Finally, we generate a set of all integers less than the known limit. The
difference of this integer set and the set of sums of abundant numbers is
the set of all integers that cannot be expressed as the sum of two abundant
numbers.
This is more or less a brute-force approach.
Answer
------
4179871
